College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 1 - Section 1.3 - Complex Numbers; Quadratic Equations in the Complex Number System - 1.3 Assess Your Understanding: 26

Answer

$\displaystyle \frac{5}{13}+\frac{12}{13}i$

Work Step by Step

Recall, $i=\sqrt{-1}$, so $i^{2}=-1$. Thus, we multiply by the conjugate of the denominator to obtain: $\displaystyle \frac{13}{5-12i}$ $\displaystyle =\frac{13}{5-12i}*\frac{5+12i}{5+12i}$ $\displaystyle=\frac{13(5+12i)}{(5-12i)(5+12i)}$ $\displaystyle =\frac{65+156i}{25+60i-60i-144i^{2}}$ $\displaystyle =\frac{65+156i}{25-144*-1}$ $\displaystyle=\frac{65+156i}{169}$ $\displaystyle =\frac{65}{169}+\frac{156}{169}i$ $\displaystyle =\frac{5}{13}+\frac{12}{13}i$
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