Chapter 1 - Section 1.3 - Complex Numbers; Quadratic Equations in the Complex Number System - 1.3 Assess Your Understanding - Page 111: 28

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

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