Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 10 - Section 10.7 - Complex Numbers - Exercise Set: 68

Answer

$\dfrac{5}{3-2i}=\dfrac{15}{13}+\dfrac{10}{13}i$

Work Step by Step

$\dfrac{5}{3-2i}$ Multiply the numerator and the denominator of this expression by the complex conjugate of the denominator: $\dfrac{5}{3-2i}=\dfrac{5}{3-2i}\cdot\dfrac{3+2i}{3+2i}=\dfrac{5(3+2i)}{3^{2}-(2i)^{2}}=\dfrac{5(3+2i)}{9-4i^{2}}=...$ Substitute $i^{2}$ with $-1$ and simplify: $...=\dfrac{5(3+2i)}{9-4(-1)}=\dfrac{5(3+2i)}{9+4}=\dfrac{15+10i}{13}=\dfrac{15}{13}+\dfrac{10}{13}i$
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