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: 64

Answer

$\dfrac{6+8i}{3i}=\dfrac{8}{3}-2i$

Work Step by Step

$\dfrac{6+8i}{3i}$ Multiply the numerator and the denominator of this expression by the complex conjugate of the denominator: $\dfrac{6+8i}{3i}=\dfrac{6+8i}{3i}\cdot\dfrac{-3i}{-3i}=\dfrac{-3i(6+8i)}{-9i^{2}}=\dfrac{-18i-24i^{2}}{-9i^{2}}=...$ Substitute $i^{2}$ with $-1$ and simplify: $...=\dfrac{-18i-24(-1)}{-9(-1)}=\dfrac{24-18i}{9}=\dfrac{24}{9}-\dfrac{18}{9}i=\dfrac{8}{3}-2i$
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