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: 31


$\displaystyle \frac{3}{4}-\frac{1}{3}i$

Work Step by Step

$\displaystyle \frac{4+9i}{12i}\qquad$ ...multiply both numerator and denominator by $-i$ $=\displaystyle \frac{4+9i}{12i}\cdot\frac{-i}{-i}$ $=\displaystyle \frac{-i(4+9i)}{-i(12i)}\qquad$ ...use the Distributive property.. $=\displaystyle \frac{(-i)(4)+(-i)(9i)}{-12i^{2}}\qquad$ ...simplify. $=\displaystyle \frac{-4i-9i^{2}}{-12i^{2}}\qquad$ ...simplify. ($i^{2}=-1$) $=\displaystyle \frac{9-4i}{12}\qquad$ ...write in standard form $=\displaystyle \frac{9}{12}-\frac{4i}{12}\qquad$ ...reduce the first fraction with $3$ and the second with $4$. $=\displaystyle \frac{3}{4}-\frac{1}{3}i$
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