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: 32


$=\displaystyle \frac{2}{13}+\frac{29}{13}i$

Work Step by Step

$\displaystyle \frac{7+4i}{2-3i}\qquad$ ...multiply both numerator and denominator by $2+3i$ $=\displaystyle \frac{(7+4i)(2+3i)}{(2-3i)(2+3i)}\qquad$ ...use the FOIL method. $=\displaystyle \frac{7\cdot 2+7\cdot 3i+4i\cdot 2+4i\cdot 3i}{2\cdot 2+2\cdot 3i+(-3i)\cdot 2+(-3i)(3i)}\qquad$ ...simplify. $=\displaystyle \frac{14+21i+8i+12i^{2}}{4+6i-6i-9i^{2}}\qquad$ ...simplify. ($i^{2}=-1$) $=\displaystyle \frac{14+29i-12}{4+9}\qquad$ ...add like terms. $=\displaystyle \frac{2+29i}{13}\qquad$ ...write in standard form $=\displaystyle \frac{2}{13}+\frac{29}{13}i$
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