Answer
Since -2 + i satisfies the equation $x^2 + 4x + 5 = 0$, it is a solution of the equation.
Work Step by Step
For -2 + i to be a solution of the equation $x^2 + 4x + 5 = 0$,
-2 + i should satisfy the equation.
Substitute $x=-2 + i$ into $x^2 + 4x + 5$, we have
$(-2+i)^2 + 4(-2+i) + 5$
= $4 -4i +i^2 -8 + 4i + 5$
= $1 + i^2$
= $1 - 1$ $(i^2 = -1)$
= $0$
= R.H.S
Therefore, -2 + i is a solution of the equation $x^2 + 4x + 5 = 0$.
