Answer
$$ -4-5j, \ or, \ -4+5j .$$
Work Step by Step
For the equation $x^2 +8x+41 = 0$, we use the quadratic formula as follows
$$ x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}, \\
a=1, \quad b=8, \quad c=41.$$
That is,
$$ x=\frac{-8 \pm \sqrt{64-4(41)}}{2 }= -4-5j, \ or, \ -4+5j .$$
