Answer
$(-2+i)^2+4(-2+i)+5=0$
Work Step by Step
In order to see that $-2+i$ is a solution, we plug it in and make sure the equation remains true.
$(-2+i)^2+4(-2+i)+5=0?$
Expand the left hand side.
$4-4i+i^2-8+4i+5$
Combine like terms using the fact that $i^2=-1$.
$(-2+i)^2+4(-2+i)+5=0$
