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: 28

Answer

$\displaystyle \frac{1}{2}+i$

Work Step by Step

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