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: 25

Answer

$\displaystyle \frac{6}{5}+\frac{8}{5}i$

Work Step by Step

Recall, $i=\sqrt{-1}$, so $i^{2}=-1$. Thus, we multiply by the conjugate of the denominator to obtain: $\displaystyle \frac{10}{3-4i}$ $\displaystyle =\frac{10}{3-4i}*\frac{3+4i}{3+4i}$ $\displaystyle =\frac{10(3+4i)}{(3-4i)(3+4i)}$ $\displaystyle =\frac{30+40i}{9+12i-12i-16i^{2}}$ $\displaystyle =\frac{30+40i}{9-16*-1}$ $\displaystyle =\frac{30+40i}{25}$ $\displaystyle =\frac{30}{25}+\frac{40}{25}j$ $\displaystyle =\frac{6}{5}+\frac{8}{5}i$
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