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: 63

Answer

$\dfrac{4-5i}{2i}=-\dfrac{5}{2}-2i$

Work Step by Step

$\dfrac{4-5i}{2i}$ Multiply the numerator and the denominator of this expression by the complex conjugate of the denominator: $\dfrac{4-5i}{2i}=\dfrac{4-5i}{2i}\cdot\dfrac{-2i}{-2i}=\dfrac{-2i(4-5i)}{-4i^{2}}=\dfrac{-8i+10i^{2}}{-4i^{2}}=...$ Substitute $i^{2}$ by $-1$ and simplify: $...=\dfrac{-8i+10(-1)}{-4(-1)}=\dfrac{-10-8i}{4}=-\dfrac{10}{4}-\dfrac{8}{4}i=-\dfrac{5}{2}-2i$
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