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: 66

Answer

$\dfrac{2-3i}{-7i}=\dfrac{3}{7}+\dfrac{2}{7}i$

Work Step by Step

$\dfrac{2-3i}{-7i}$ Multiply the numerator and the denominator of this expression by the complex conjugate of the denominator: $\dfrac{2-3i}{-7i}=\dfrac{2-3i}{-7i}\cdot\dfrac{7i}{7i}=\dfrac{7i(2-3i)}{-49i^{2}}=\dfrac{7(2i-3i^{2})}{-49i^{2}}=...$ Substitute $i^{2}$ with $-1$ and simplify: $...=\dfrac{7[2i-3(-1)]}{-49(-1)}=\dfrac{7(2i+3)}{49}=\dfrac{2i+3}{7}=\dfrac{3}{7}+\dfrac{2}{7}i$
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