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: 55


$-\displaystyle \frac{5}{26}-\frac{51}{26}i$

Work Step by Step

$\displaystyle \frac{(5-2i)+(5+3i)}{(1+i)-(2-4i)}\qquad$ ...remove parentheses using the distributive property. $=\displaystyle \frac{5-2i+5+3i}{1+i-2+4i}\qquad$ ...add like terms. $=\displaystyle \frac{10+i}{-1+5i}\qquad$ ...rationalize by multiplying both the numerator and denominator with $-1-5i$. $=\displaystyle \frac{10+i}{-1+5i}\cdot\frac{-1-5i}{-1-5i}$ $=\displaystyle \frac{(10+i)(-1-5i)}{(-1+5i)(-1-5i)}\qquad$ ...use the FOIL method. $=\displaystyle \frac{-10-50i-i-5i^{2}}{1+5i-5i-25i^{2}}\qquad$ ...simplify and add like terms ($i^{2}=-1$). $=\displaystyle \frac{-5-51i}{26}\qquad$ ...write in standard form $a+bi$ $=-\displaystyle \frac{5}{26}-\frac{51}{26}i$
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