Answer
$x=-1\pm i$
Work Step by Step
Our aim is to compute the zeros by solving the equation
$x^2+2x+2=0$
We need to complete the square.
$(x^2+2x+1)+1=0\\(x+1)^2+1=0\\(x+1)^2=-1$
Taking the square root of both sides, we get:
$(x+1)=\pm i \implies x=-1\pm i$
