Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 4 Quadratic Functions and Factoring - 4.6 Perform Operations with Complex Numbers - 4.6 Exercises - Skill Practice - Page 280: 30


$-\displaystyle \frac{5}{3}+\frac{2}{3}i$

Work Step by Step

$\displaystyle \frac{-2-5i}{3i}\qquad$ ...multiply both numerator and denominator by $-i$ $\displaystyle \frac{(-2-5i)(-i)}{3i(-i)}\qquad$ ...use the FOIL method. $=\displaystyle \frac{(-2)(-i)+(-5i)(-i)}{-3i^{2}}\qquad$ ...simplify. $=\displaystyle \frac{2i+5i^{2}}{-3i^{2}}\qquad$ ...simplify. ($i^{2}=-1$) $=\displaystyle \frac{2i-5}{3}\qquad$ ...write in standard form $=-\displaystyle \frac{5}{3}+\frac{2}{3}i$
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