Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 4 Quadratic Functions and Factoring - 4.7 Complete the Square - 4.7 Exercises - Quiz for Lessons 4.5-4.7 - Page 291: 11


$\displaystyle \frac{-44}{157}-\frac{24}{157}i$

Work Step by Step

$\displaystyle \frac{4i}{-6-11i}\qquad$ ...rationalize by multiplying both the numerator and denominator with $-6+11i$. $=\displaystyle \frac{4i(-6+11i)}{(-6-11i)(-6+11i)}\qquad$ ...use the FOIL method. $=\displaystyle \frac{-24i+44i^{2}}{(-6-11i)(-6+11i)}\qquad$ ...difference of squares: $(a+b)(a-b)=a^{2}-b^{2},a=-6, b=11i$ $==\displaystyle \frac{-24i+44i^{2}}{(-6)^{2}-(11i)^{2}}\qquad$ ...simplify. ($i^{2}=-1$) $=\displaystyle \frac{-24i-44}{36+121}\qquad$ ...add like terms. $=\displaystyle \frac{-44-24i}{157}\qquad$ ...write in standard form. $=\displaystyle \frac{-44}{157}-\frac{24}{157}i$
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