Answer
The proof is below.
Work Step by Step
Using the quadratic formula:
$$ x_{1,\:2}=\frac{-7\pm \sqrt{7^2-4\left(-1\right)\left(-13\right)}}{2\left(-1\right)} \\ x=\frac{7}{2}-i\frac{\sqrt{3}}{2},\:x=\frac{7}{2}+i\frac{\sqrt{3}}{2}$$
Thus, we see that the two solutions are imaginary.