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: 28


$\displaystyle \frac{7}{65}+\frac{56}{65}i$

Work Step by Step

$\displaystyle \frac{7i}{8+i}\qquad$ ...multiply both numerator and denominator by $8-i$ $=\displaystyle \frac{7i(8-i)}{(8+i)(8-i)}\qquad$ ...use the FOIL method. $=\displaystyle \frac{7i\cdot 8-7i\cdot i}{8\cdot 8+8\cdot(-i)+i\cdot 8+i\cdot(-i)}\qquad$ ...simplify. $=\displaystyle \frac{56i-7i^{2}}{64-8i+8i-i^{2}}\qquad$ ...simplify. ($i^{2}=-1$) $=\displaystyle \frac{7+56i}{65}\qquad$ ...divide with 65 $=\displaystyle \frac{7}{65}+\frac{56}{65}i$
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