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: 33


$-\displaystyle \frac{59}{106}-\frac{21}{106}i$

Work Step by Step

$\displaystyle \frac{-1-6i}{5+9i}\qquad$ ...multiply both numerator and denominator by $5-9i$ $=\displaystyle \frac{(-1-6i)(5-9i)}{(5+9i)(5-9i)}\qquad$ ...use the FOIL method. $=\displaystyle \frac{-5+9i-30i+54i^{2}}{25-45i+45i-81i^{2}}\qquad$ ...simplify. ($i^{2}=-1$) $=\displaystyle \frac{-5+9i-30i-54}{25-45i+45i+81}\qquad$ ...add like terms. $=\displaystyle \frac{-59-21i}{106}\qquad$ ...write in standard form $=-\displaystyle \frac{59}{106}-\frac{21}{106}i$
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