Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Appendix G - Complex Numbers - G Exercises: 7

Answer

$\frac{11}{13}+\frac{10}{13}i$

Work Step by Step

$\displaystyle \frac{1+4i}{3+2i}$ We multiply the numerator and denominator by the conjugate of the denominator: $=\frac{1+4i}{3+2i}\cdot\frac{3-2i}{3-2i}$ We use the fact that $i^2=-1$ (because $i=\sqrt{-1}$) $=\frac{3-2i+12i-8*-1}{3^{2}+2^{2}}$ $=\frac{11+10i}{13}$ $=\frac{11}{13}+\frac{10}{13}i$
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