Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 7 - Section 7.7 - Complex Numbers - Exercise Set: 82

Answer

$\dfrac{4}{5}-\dfrac{3}{5}i$

Work Step by Step

Multiply both the numerator and the denominator by the conjugate of the denominator, which is $-5i$, to obtain: $=\dfrac{(3+4i)(-5i)}{5i(-5i)} \\=\dfrac{-15i-20i^2}{-25i^2}$ Use the fact that $i^2=-1$ to obtain: $=\dfrac{-15i-20(-1)}{-25(-1)} \\=\dfrac{-15i+20}{25} \\=\dfrac{20-15i}{25} \\=\dfrac{20}{25} - \dfrac{15}{25}i \\=\dfrac{4}{5}-\dfrac{3}{5}i$
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