Answer
$\frac{1}{2}+i$
Work Step by Step
Multiply the numerator and the denominator by the conjugate of $-2i$ which is $2i$.
$\dfrac{2-i}{-2i}=\dfrac{2-i}{-2i}\cdot \dfrac{2i}{2i}$
Use distributive property in the numerator.
$=\dfrac{4i-2i^2}{-4i^2}$
Use $i^2=-1$.
$=\dfrac{4i-2(-1)}{-4(-1)}$
Simplify.
$=\dfrac{4i+2}{4}$
$=\dfrac{4i}{4}+\dfrac{2}{4}$
$=i+\dfrac{1}{2}$
Hence, the solution in the standard form is $\frac{1}{2}+i$.
