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: 30


$x=3$ or $x=-2$ $y=-3$ or $y=3$

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: $(x^{2}-6)-x+9i-y^{2}i=0$ 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 $(x^{2}-6)-x=0$, can be factorized to $(x-3)(x+2)=0$, which gives $x=3$ or $x=-2$ The imaginary part of the expression $9-y^{2}=0$, can be simplified to $9-y^{2}=0$. The expression can be factorized to $(3-y)(3+y)=0$, which gives $y=-3$ or $y=3$
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