Calculus 8th Edition

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

Appendix G - Complex Numbers - G Exercises: 8

Answer

$-\frac{5}{17}+\frac{14}{17}i$

Work Step by Step

$\displaystyle \frac{3+2i}{1-4i}$ We multiply the numerator and denominator by the conjugate of the denominator: $=\frac{3+2i}{1-4i}\cdot\frac{1+4i}{1+4i}$ We use the fact that $i^2=-1$ (because $i=\sqrt{-1}$) $=\frac{3+12i+2i+8*-1}{1^{2}+4^{2}}$ $=\frac{-5+14i}{17}$ $=-\frac{5}{17}+\frac{14}{17}i$
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