Answer
is a solution
Work Step by Step
Substituting $x$ with $-1+i$ in given equation, $
x^2+2x=-2
,$ then
\begin{array}{l}\require{cancel}
(-1+i)^2+2(-1+i)=-2
\\\\
[(-1)^2+2(-1)(i)+i^2]+(-2+2i)=-2
\\\\
[1-2i+(-1)]+(-2+2i)=-2
\\\\
(1-1-2)+(-2i+2i)=-2
\\\\
-2+0=-2
\\\\
-2=-2
\text{ (TRUE)}
.\end{array}
Since the solution above ended with a TRUE statement, then $-1+i$ $\text{
is a solution
}$ to the given equation.
