College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 1 - Section 1.3 - Complex Numbers; Quadratic Equations in the Complex Number System - 1.3 Assess Your Understanding: 27

Answer

$1-2i$

Work Step by Step

Recall, $i=\sqrt{-1}$, so $i^{2}=-1$. Thus, we multiply by $\frac{-i}{-i}$ to obtain: $\displaystyle \frac{2+i}{i}$ $\displaystyle =\frac{2+i}{i}*\frac{-i}{-i}$ $\displaystyle=\frac{-i(2+i)}{-i*i}$ $\displaystyle =\frac{-2i-i^{2}}{-i^{2}}$ $\displaystyle=\frac{-2i-(-1)}{-(-1)}$ $\displaystyle=\frac{-2i+1}{1}=1-2i$
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