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: 61


$\displaystyle \frac{ac+bd}{c^{2}+d^{2}}+\frac{bc-ad}{c^{2}+d^{2}}i$

Work Step by Step

$\displaystyle \frac{a+bi}{c+di}\qquad$ ...rationalize by multiplying both the numerator and denominator with $c-di$. $=\displaystyle \frac{(a+bi)(c-di)}{(c+di)(c-di)}\qquad$ ...use the FOIL method $=\displaystyle \frac{ac-adi+bci-bdi^{2}}{c^{2}-cdi+cdi-d^{2}i^{2}}\qquad$ ...simplify ($i^{2}=-1$). $=\displaystyle \frac{ac-adi+bci+bd}{c^{2}+d^{2}}\qquad$ the real and imaginary parts in the numerator. $=\displaystyle \frac{ac+bd+(bc-ad)i}{c^{2}+d^{2}}\qquad$ ...write in standard form $a+bi$ $=\displaystyle \frac{ac+bd}{c^{2}+d^{2}}+\frac{bc-ad}{c^{2}+d^{2}}i$
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