Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 8 - Section 8.1 - Complex Numbers - 8.1 Problem Set - Page 425: 29

Answer

$x=4$ or $x=-2$ $y=1$

Work Step by Step

In order to solve the question, the key step here is to compare and observe the individual parts - imaginary and real parts. bringing all the terms to one side, we have: $(x^{2}-2x)-8+y^{2}i-(2y-1)i=0$ since the total sum of the real and imaginary parts are equal to $0$, this implies that the sum of the real parts is equal to $0$ and the sum of the imaginary part is equal to $0$ Therefore, The real part of the expression $(x^{2}-2x)-8=0$, can be factorized to $(x-4)(x+2)=0$, which gives $x=4$ or $x=-2$ The imaginary part of the expression $y^{2}-(2y-1)=0$, can be simplified to $y^{2}-2y+1=0$. The expression can then be factorized to $(y-1)^{2}=0$, which gives $y=1$
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