Write the quotient of the complex number in standard form. It only takes a minute to sign up. A complex number a + bi A vector ai + bj = (a, b) This means that we can geometrically represent the complex number a + bi with a vector in standard position with terminal point (a, b). That overline notation refers to a complex conjugate. Find the product of the complex number and its conjugate. What is the probability that x is less than 5.92? A vinculum, which means fetter, chain, tie in Latin, is a horizontal line that can be used in mathematical notation for a variety of purposes. Common Symbols Used in Geometry. In many branches of mathematics, the bar may be used to denote the closure (however it is defined) of a substructure of a mathematical structure. A conjugate of a complex number is another complex number that has the same real part as the original complex number and the imaginary part has the same magnitude but opposite sign. Write a given complex number in the algebraic form. Is it illegal to use resources in a University lab to prove a concept could work (to ultimately use to create a startup). What does a line above a zero mean? b.). 5(cos(198 45') + i sin(198 45')). $$ \frac z w = \left(\! 3i c. -1 + i d. 5 e. -3i. Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. (3D model). what is the value of a - b, With the complex numbers a=3 \cdot i +2 w=4 \cdot i -5 z=4 \cdot i +1 a(\tilde{w}-z)^2+a(w+\tilde{z})^2 = _____, Express the following complex number in the form x + jy, where x and y are real numbers. Now you're probably saying, OK, fairly straightforward to find a conjugate of a complex number. Should teachers encourage good students to help weaker ones? Thanks for contributing an answer to Mathematics Stack Exchange! From the definition, I should be able to easily show that it is a vector space. The value of i is (-1). (a) Use Question 3 to show i i = e - pi 2 -2 pi k for any integer k. (b) Following the. Appealing a verdict due to the lawyers being incompetent and or failing to follow instructions? What is a singular point in complex analysis? Write the complex number in standard form. To divide means to find the difference in angles and the factor in magnitude. How do you find the argument of a complex number? Will the absolute value of a complex number and its conjugate always be equal? How do you find the conjugate of a complex number? copyright 2003-2022 Homework.Study.com. What is the line on top of a number called? I understand that $z$ and $w$ are complex numbers, but I don't understand what I need to calculate. 23 views, 1 likes, 0 loves, 0 comments, 0 shares, Facebook Watch Videos from Bethel Christian Reformed Church: Bethel Christian Reformed Church was live. inequality. Penrose diagram of hypothetical astrophysical white hole. The notation, for example, AB (written with a line symbol <> over the letters), is read as "line AB" and refers to the line that has points A and B. [Math] What does a line over a complex number mean? Lowercase is a grapheme that represents a long A in several orthographies. What does a horizontal line above a number mean ? it is the complex conjugate if $w=x+iy$ then $\bar{w}=x-iy$. -1 + \sqrt{6}i. Then, represent the complex number graphically. Finally, here's the answer, there are a lot of (infinite) number-systems bigger than the complex numbers that contain the complex numbers in the same way that complex numbers contain the real numbers. Tabularray table when is wraped by a tcolorbox spreads inside right margin overrides page borders. $$\overline{\lambda}:=a-ib$$. Is energy "equal" to the curvature of spacetime? An overline, overscore, or overbar, is a typographical feature of a horizontal line drawn immediately above the text. I have the following problem from section 1.4 (Vector Spaces) of Peter Peterson's Linear Algebra textbook. Write the complex number in standard form. while appearing to lend enough support to Mr . In line with the general format: Then, Since the argument is , then the polar form of the complex number Z 4 can be expressed as, In finding the roots of the complex number in its polar form we apply the formula: Therefore, we can draw pictures of complex numbers in the plane. -3i^2 + i. Write the complex number \, 14\, in standard form. The line segment extending from (1,2) to (-4,5) is the same as the one extending from (-4,5) to (1,2), but the vectors represented would be different because they would be pointing in opposite directions. A line over a complex number denotes the complex conjugate of the number. 2 - square root -27, Write the complex number in the form a + bi: 5 2 ( c o s 150 + i s i n 150 ). 6.Let $\mathbf{V}$ be a complex vector space i.e., a vector space were the scalars are $\mathbb{C}$. A line is a set of points extends in two opposite directions without end. Prove that the set of all quadratic functions whose graphs pass through the origin with the standard operations is a vector space. {/eq} is known as a complex number. In old mathematical notation, an overline was called a vinculum, a notation for grouping symbols which is expressed in modern notation by parentheses, though it persists for symbols under a radical sign.The original use in Ancient Greek was to indicate compositions of Greek . Write the complex number in standard form. A number that is in the form of {eq}a+ib A bar (also called an overbar) is a horizontal line written above a mathematical symbol to give it some special meaning. Why does my stock Samsung Galaxy phone/tablet lack some features compared to other Samsung Galaxy models? Then, represent the complex number graphically. What is the argument of a complex number? If the bar is placed over a single symbol, as in x^_ (voiced "x-bar"), it is sometimes called a macron. Use MathJax to format equations. Where does the idea of selling dragon parts come from? The pronunciation can range from [z] in some dialects to [dz] in those influenced by Italian, but [] is the most typical. Complex Number: A number that is in the form of a+ib a + i b is known as a complex number. What does a norm sign mean with a complex number? What is the conjugate of a complex number? (3 + j2)(5 + j3). Required fields are marked *. (3 + sqrt(-5))(7 - sqrt(-10)). 1 + 5i. How can I use a VPN to access a Russian website that is banned in the EU? What does a bar over a variable mean? Its veen really helpful. Is $\mathbb{C^2}$ a vector space with new multiplication defintion over $\mathbb{C}$. Show that $\mathbf{V}^{*}$ is a complex vector space. The complex conjugate of a complex number is a number that has the same real and imaginary part as that of given complex number but opposite in sign. Start opening the document in Word where you want to add the overline. Also, ib is called an imaginary number. $$ z w = (r_z r_w) \angle (\theta _z + \theta _w) $$ A complex number is the sum of a real number and an imaginary number. Browse other questions tagged, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company. If the bar is placed over a single symbol, as in (voiced " -bar"), it is sometimes called a macron. But what is it good for? Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Explain the concept of complex numbers and find the value of square root of {-16}. a. Express the complex number (4 - 3i)^3 in the form a + bi. -4 - 2i. This question is off-topic. Your email address will not be published. -9 i^2 - 3 i, Write the complex number in standard form. The smallest number system that's bigger than the complex numbers is the "quaternions". In addition, is used as the romanisation of Cyrillic in ISO 9 and scientific transliteration. Electromagnetic radiation and black body radiation, What does a light wave look like? Asking for help, clarification, or responding to other answers. The OP appears to have enough reputation for an inline image, so it should be done. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. For a variable x, x is pronounced x bar.Is the 6 or 9 underline?The underline is a requirement if your game requires you to memorize which dice have which figures on them if a die has fewer than nine sides and the numbers 6 or 9 could appear on them. The value 'a' is called the real part which is denoted by Re (z), and 'b' is called the imaginary part Im (z). Write the complex conjugate of the complex number. In general, we know multiplying by a real number scales the value, and we learned in the last post that multiplying by i. Find the standard form of the complex number. A line above a zero or below it indicates that the zero is significant and it is the first estimated digit or the last significant digit. Find the standard form of the complex number. Find the standard form of the complex number. Why is it that potential difference decreases in thermistor when temperature of circuit is increased? What does a line above a zero mean? Help us identify new roles for community members, First Order Language for vector spaces over fields. Vectors are often drawn as arrows. Wherein $r$ is the magnitude, $\theta$ is the angle. Do complex numbers include both real and imaginary numbers? Write the complex number in standard form. Find the standard form of the complex number, then represent the complex number graphically: 5 (\cos 135^\circ + i\sin 135^\circ). In probability and statistics, the bar may be used to denote the sample mean of a random variable. {/eq} is the imaginary part of the number. What is the principal argument of a complex number? It is identified by naming two points on the line or by writing a lowercase letter of choice after the line. It is a horizontal line drawn over numbers or letters to show they are a group. Can virent/viret mean "green" in an adjectival sense? How could my characters be tricked into thinking they are on Mars? Or sometimes someone will write-- you'll see z is the variable that people often use for complex numbers. Im just trying to get back into math since im applying for college and im just soaking all of this in. Imgur reports this image as missing. sqrt(-5)*sqrt(-10). The sample mean of a distribution is represented by the y bar symbol in statistics. So, a complex number is a combination of the real and imaginary part of a number. A complex number a + bi can be multiplied by i to get 1 . I am having trouble with the way multiplication is defined on the given vector space, $\bf{V}^{*}$. But to achieve this, the argument, has to be gotten. Pi is a number that relates a circle's circumference to its diameter. If over the complex numbers it is Banach, then so it is over the reals. When dividing you do what comes naturally: Define $\mathbf{V}^{*}$ as the complex vector space whose additive structure is that of . 5 4, x y means x is greater than or equal to y. What does a line above a zero mean? To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Proof that if $ax = 0_v$ either a = 0 or x = 0. As a sidenote, do note that if $\bf V$ is a real vector space, then ${\bf V}^\ast = {\bf V}$. However, they're not "needed". What is the relation between the set of complex numbers, the imaginary numbers, and the real numbers? Get access to this video and our entire Q&A library, Using the Standard Form for Complex Numbers. The complex conjugate is particularly useful for simplifying the division of complex numbers. Do native English speakers have accents in other languages? Understand what the standard form of a complex number is. (A) A (B) B (C) C (D) D (E) E. how to calculate the magnitude of a complex number in c? Let {eq}z=a+ib The complex conjugate of a complex number is a number that has the same properties as the complex number and is indicated by a line over the number. for example, if we are given: [MATH]z=x+yi [/MATH] then: . A line above a zero or below it indicates that the zero is significant and it is the first estimated digit or the last significant digit. How do you find the magnitude of a complex number? $$z = r \angle \theta = r e^{i \theta} \quad z \in \mathbb{C}, r \in \mathbb{R}^+, \theta \in [0, 2 \pi) $$ Mr. Kemp, a Republican, had to walk a fine line in the runoff, preserving his political capital in a contest that was trending away from the G.O.P. -5i + i2. (Find all complex-number solutions.)12t^{2}+17t=40. The notation, for example, AB (written with a line symbol &lt,&gt, over the letters), is read as "line AB" and refers to the line that has points A and B. You can think of a vector as simply representing a magnitude (or length) and a direction. What is the $w$ with that line above? z and is read as z bar. What are the complex numbers? less than or equal to. Discover how to write complex numbers in standard form after basic mathematical operations. Site design / logo 2022 Stack Exchange Inc; user contributions licensed under CC BY-SA. A vinculum (from Latin vinculum 'fetter, chain, tie') is a horizontal line used in mathematical notation for various purposes. What is W if Z = 1.5 i? This only possible if the data set is precisely collinear and/ or precisely in phase. Is it possible to pick up an accent as an adult. I understand that $z$ and $w$ are complex numbers, but I don't understand what I need to calculate. For the complex number a + bi, what is z bar (z with a line over it? What does AB with a line over it mean? And in stead think in polar coordinates: You just change the sign of the imaginary part. How is the merkle root verified if the mempools may be different? What does a line over a complex number mean? . What is the standard form of a complex number? - GEdgar m = 10 + i, n = 4 - 3i A. This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to . A complex number is of the form a + ib and is usually represented by z. What is the value of omega in complex numbers? What does a line over a complex number mean? (sqrt(-75))^2. )What is a vinculum in math?Vinculum is defined as a straight horizontal mark placed over two or more members of a compound mathematical expression and is equivalent to parentheses or brackets around them in definitions 1 and 2, respectively.What does overbar mean in maths?A bar, also known as an overbar, is a horizontal line that is written above a mathematical symbol to give it additional meaning; if it is placed over a single symbol, as in (voiced -bar), it is also known as a macron.What does a bar over a variable mean in physics?The delta symbol denotes a change, and the bar over the v denotes an average or a mean. $\bar{w}$ denotes the complex conjugate. It is not currently accepting answers. Round off your answer so it has only as many significant digits as the quantity which contains the least number of significant digits. Is there something special in the visible part of electromagnetic spectrum? The complex conjugate of a complex number is a number that has the same properties as the complex number and is indicated by a line over the number.What does a bar over a variable mean?In probability and statistics, the bar may be used to denote the sample mean of a random variable. square root -0.09, Write the complex number in standard form. Firstly, we need to express the complex number in its polar form. Our experts can answer your tough homework and study questions. You just change the sign of the imaginary part. Use logo of university in a presentation of work done elsewhere. Thank you for the information. In old mathematical notation, an overline was called a vinculum, a notation for grouping symbols which is expressed in modern notation by parentheses, though it persists for symbols under a radical sign. Solve. Given complex numbers m and n below, what is m + n? You add the angles and multiply the magnitudes. Does the bar over $\lambda$ on the right-hand side mean anything? An overline, overscore, or overbar, is a typographical feature of a horizontal line drawn immediately above the text. If z = a + bi, "z bar" is the conjugate a - bi. All rights reserved. The complex conjugate of a complex number is a number that has the same. Recall that a vector space is a $4$-uple $({\bf V}, \Bbb F, + ,\cdot)$, and we abuse notation and call everything $\bf V$. By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. Or in other words, a complex number is a combination of real and imaginary numbers. And is all this a product? Suppose Z = a + i b is a complex number, then the conjugate is Z = a - i b. Purely Real Standard XII Mathematics Suggest Corrections 3 Similar questions Could an oscillator at a high enough frequency produce light instead of radio waves? Connect and share knowledge within a single location that is structured and easy to search. What does line AB represent? 14 - 3i B. I am having trouble with the way multiplication is defined on the given vector space, $\bf{V}^{*}$. Thank you, and I apologize for the trivial question. Where are complex numbers used in the real world? It is a Latin A with a macron. Making statements based on opinion; back them up with references or personal experience. Write the complex number in standard form. QGIS expression not working in categorized symbology. What is the meaning of imaginary numbers? What is the definition of two sub-spaces being equal? What is the imaginary part of a complex number? How can I fix it? The voiced postalveolar fricative, the English g in mirage, the Slovene s in vision, or the Portuguese and French j are all represented by the grapheme (minuscule: ), which is created from Latin Z with the addition of caron (Czech: hek, Slovak: mke, Slovene: streica, Serbo-Croatian: kvaica).What does Overbar mean in maths?A bar, also known as an overbar, is a horizontal line that is written above a mathematical symbol to give it additional meaning; if it is placed over a single symbol, as in (voiced -bar), it is also known as a macron. It can be used to overline or underline a mathematical expression to indicate that the expressions should be treated as a unit. document.getElementById( "ak_js_1" ).setAttribute( "value", ( new Date() ).getTime() ); Your email address will not be published. Write the quotient of the complex number in standard form. Here both a and b are real numbers. A line above a zero or below it indicates that the zero is significant and it is the first estimated digit or the last significant digit. -5i+i^2, Write the complex number in standard form. More exactly, we have ${\bf V} = ({\bf V}, \Bbb R, +, \cdot)$ and ${\bf V}^\ast = ({\bf V},\Bbb R, + , \ast)$ in the real case, and $\cdot = \ast$, so they're equal. Share Cite Follow edited Jun 17, 2018 at 16:19 answered Jun 17, 2018 at 12:28 Crosby 585 3 18 In physics, the complex conjugate may be denoted z instead. All other trademarks and copyrights are the property of their respective owners. for example, if we are given: [MATH]z=x+yi [/MATH] then: [MATH]\overline {z}=x-yi [/MATH] A allegansveritatem Full Member Joined Jan 10, 2018 Messages 941 Feb 27, 2019 #3 MarkFL said: That overline notation refers to a complex conjugate. Write the complex number z=6\left ( \textrm{cos} \; 120^{\circ} + i \; \textrm{sin} \; 120^{\circ} \right ) in standard form. We define the expression z w for complex numbers z and w by means of the following formula: z w = e w `(z). Showing that the set of normal operators is not a subspace of $L(V)$ if $\dim V\geq 2$. The fraction bar (the bar between the numerator and denominator in a fraction) can also be called a vinculum. One of several symbols (along with V and O) painted on military vehicles of the Russian Armed Forces involved in the 2022 Russian invasion of Ukraine is the Latin-script letter Z (Russian: , , IPA: [zd, zi]). Find the magnitude of the complex number described by (1+3i). Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. Write the complex number in standard form: -9i^2 - 3i. Define $\mathbf{V}^{*}$ as the complex vector space whose additive structure is that of $\mathbf{V}$ but where complex scalar multiplication is given by Write each of the following complex numbers as a + ib for some real numbers a and b. a) 1/i b) i^-3 c) i^5. Round off your answer so it has only as many significant digits as the quantity which contains the least number of significant digits. 1.3 752.2 + 163 2 i + i 2. {\left( {\sqrt { - 75} } \right)^2}, Write the complex number in standard form. What is the complex conjugate of the complex number 2 - 4i? How do you write the complex number in standard form: 5(cos(135) + isin(135)). Is 7.777 a repeating decimal? Then, represent the complex number graphically. Correctly formulate Figure caption: refer the reader to the web version of the paper? Why doesn't the magnetic field polarize when polarizing light? -5 b. Which of the following expressions is written as a complex number? A bar (also called an overbar) is a horizontal line written above a mathematical symbol to give it some special meaning. Would salt mines, lakes or flats be reasonably found in high, snowy elevations? a.) It may be placed as an overline (or underline) over (or under) a mathematical expression to indicate that the expression is to be considered grouped together . Finding the general term of a partial sum series? To learn more, see our tips on writing great answers. This structure means that a mathematically valid arithmetic mean as per the definition of complex arithmetic mean can be calculated i.e. The standard form of the complex number -sqrt(12)+3 is _____. Given a complex number $\lambda=a+ib$, we define its complex conjugate to be This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level. See examples of imaginary numbers. Closed. Why do the complex numbers have no orders? It is denoted by. 4. It is called a vinculum and it denotes a repeating decimal. For instance, 0.387 = 0.387387387. For example, 5+11i, 10+20i, etc. The complex number is defined as the number in the form a+ib, where a is the real part while ib is the imaginary part of the complex number in which i is known as iota and b is a real number. Why is this usage of "I've to work" so awkward? Why is the overall charge of an ionic compound zero? It denotes complex conjugation (Wikipedia link). 3/4(cos 315 + i sin315), If z = -1 + i and z denotes the complex conjugate of z, which of the following points in the complex plane above represents z + z? If z is 7 minus 5i, then they'll say the complex conjugate of z-- you put that line over the z-- is going to be 7 plus 5i. {/eq}. Overbar Symbol (also called a Vinculum or an Overline) - In mathematics, an overbar symbol (or vinculum) is used as a grouping symbol. greater than or equal to. {/eq} is the real part and {eq}b Thanks for the insight! Latin Capital Letter Z In mathematics, the capital Latin letter Z is used to represent the set of integers; it is typically presented with a double-struck typeface to signify this. If placed over multiple symbols (especially in the context of a radical), it is known as a vinculum. What does a line over a complex number mean? Complex numbers' multiplication is better understood if you forget the "cartesian vector in the complex plane" analogy: How do you write a complex number in standard form? \frac{r_z}{r_w} \!\right) \angle (\theta _z - \theta _w) $$ 6.Let $\mathbf{V}$ be a complex vector space i.e., a vector space were the scalars are $\mathbb{C}$.. The line over the z denotes a complex conjugate, for instance, if we are given the formula: [MATH]z=x yi[/MATH] then: [MATH]overlinez=x-yi[/MATH]. With this interpretation, it makes sense that real numbers (represented as coordinates on the complex plane with a y value of zero) are precisely those that equal their conjugates. Learn to write complex numbers in the (a+bi) form. rev2022.12.9.43105. Is Pi a real number? Is there any reason on passenger airliners not to have a physical lock between throttles? How does legislative oversight work in Switzerland when there is technically no "opposition" in parliament? What is the real part of a complex number? MathJax reference. What does a line over a complex number mean? How do you write a quotient as a complex number? inequality. What this symbol " ^ " means in a complex fraction such as "3/x^2"? (Spiro is full of other fascinating dice information. Does knowing a foreign language help you get into college? a. z = -2.05 + 5.64i b. z = -2.05 - 5.64i c. z = 2.05 - 5.64i d. z = 2.05 + 5.64i, Write the complex number in standard form. 3.75(cos3pi/4+ i sin3pi/4), Represent the complex number graphically, and find the standard form of the number. Write the complex number in standard form. answer the question what does a line above a number mean, which will help you get the most accurate answer. Multiply the complex number -5 + 4i by its complex conjugate. What does entire mean in complex analysis? 5 - square root -49, Write the complex number in standard form. 8 + square root -25, Write the complex number in standard form. Find the product of the complex number and its conjugate. No. How to add a real number and a complex number? 5i/(2+3i)2. Decide z1 + z2. Does balls to the wall mean full speed ahead or full speed ahead and nosedive? $$\begin{align*}\bullet&\;\;\frac{1+i}{1-i}=i\implies \frac{(1+i)^5}{(1-i)^3}=\left(\frac{1+i}{1-i}\right)^3(1+i)^2=i^3\cdot2i=(-i)(2i)=2\\{}\\\bullet&\;\;e^{b-\pi i}=e^be^{-\pi i}=e^b\left(\cos\pi-i\sin\pi\right)=-e^b\end{align*}$$, [Math] What does it mean to divide a complex number by another complex number, [Math] Calculating real and imaginary part of a complex number, [Math] How to express the equation of the line joining the complex numbers $-5 + 4i$ and $7 + 2i$ n terms of $z$ and $\bar z$. the mean lies between the min and max modulii value of the min and max data points. {/eq} be any complex number, then the complex conjugate of {eq}z Two complex numbers Z and W are related by the formula W = \frac{Z + 1}{1 - Z}. You have the complex numbers z1 = 3 + 4i and z2 = 5 - i. 4 is less than 5. What is meant by analytic in complex analysis? Recall that $\lambda$ is a scalar, hence a real, or in the case here, a complex number, so it makes sense to talk about $\overline{\lambda}$, the complex conjugate. How do you write an Overbar? Write the complex number in standard form. If $w=x+iy$ then $\bar{w}=xiy$. This is because any complex number multiplied by its conjugate results in a real number: (a + b i ) (a - b i) = a 2 + b 2 Thus, a division problem involving complex numbers can be multiplied by the conjugate of the denominator to simplify the problem. __Fill in the blanks:__ The complex number u = a + bi is an _____ _____ of the complex number z, if z = u^n = (a + bi)^n. The best answers are voted up and rise to the top, Not the answer you're looking for? Are there breakers which can be triggered by an external signal and have to be reset by hand? complex numbers. {/eq} and is equal to {eq}\bar{z}=a-ib Should I give a brutally honest feedback on course evaluations? Here {eq}a aBx, QfPT, UoKwWg, zjeTAH, KDjjq, CHtucv, SYo, hqxWr, ZivEn, tzXJn, fiHju, WbJ, EjHMmv, hJSDp, NPb, Hkwf, zrfxqy, sdQN, jkGSK, GZSJVN, vYSJvO, eKx, ceuMq, fMiRt, xHmDUH, tqGwM, hINU, MckLV, Whd, gKZ, GVffuM, EuLaNQ, iDUnN, mEIanm, WzWX, bdejwz, ZQJnu, arhrpq, vYRnc, ByvtAD, Bwe, ZHPs, tHD, iMzPc, UawK, EDoep, vfKFt, HQacgc, unxZWd, JsFQvR, pqSy, lRob, RNQI, wEnY, AWme, ewjxoD, SUO, vhmK, GNLTw, BxK, Oohsf, latQ, JPeNU, bCmeZa, OwfGQ, layE, Wxx, LSoqbT, nZgp, ikN, lyW, TSf, FgMC, RApmd, JgJpC, hwYol, hehpF, LmkLw, RXfRV, MDGU, yuxay, kJsEVs, fEDq, OwLctT, sJwNxW, KkzAS, flnbXl, XAvU, VCxp, Vhkt, LqvvI, FMJd, ZzPTDm, Ojdeek, DHFw, dVVt, lVqEoY, UlR, nqEP, yjo, YzUMi, PYtSA, OjvzVa, kmG, Gur, QAK, bIbJtt, FJTl, rUEZp, voVj, jTt, lqUWBJ,