Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Appendix A - Review - A.11 Complex Numbers - A.11 Assess Your Understanding - Page A94: 25

Answer

$1-2i$

Work Step by Step

Multiply both the denominator and the numerator by $-i$, which is the conjugate of $i$, then use the fact that $i^2=-1$ to obtain: \begin{align*} &=\frac{2+i}{i}\cdot\frac{-i}{-i}\\ \\&=\frac{(2+i)(-i)}{-i^2}\\ \\&=\frac{-2i-i^2}{-(-1)}\\ \\&=\frac{-2i-(-1)}{1}\\ \\&=\frac{-2i+1}{1}\\ \\&=1-2i \end{align*}
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