Решить уравнение с комплексными числами

$
z^{2} + (2i- 7)z + 13 - i = 0
\\\\
$
Найдем дискриминант
$
D = (2i - 7)(2i - 7) - 4(13 - i) = -4 - 28i + 49 - 52 + 4i = -7 - 24i
\\\\
-7 - 24i = w^{2} = (a + bi)^2 = a^2 + 2abi - b^{2}
\\\\
\begin{cases}
a^2 - b^2 = -7
\\
ab = -12
\end{cases}
\\\\
a = \frac{-12}{b}
\\\\
144 - b^4 = -7b^2
\\
b^4 - 7b^2 - 144 = 0
\\
b^2 = c
\\
c^2 - 7c - 144 = 0
\\
D = 49 + 576 = 625
\\
c_{1} = -9, c_{2} = 16
\\
b = 4, a = -3, w = -3 + 4i
\\
b = -4, a = 3, w = 3 - 4i
\\
z_{1} = \frac{-2i + 7 - (-3 + 4i)}{2} = \frac{10 - 6i}{2} = 5 - 3i
\\
z_{2} = \frac{-2i + 7 - 3 + 4i)}{2} = \frac{2i + 4}{2} = i + 2
\\
\textbf{Ответ: }\mathbf{z_{1} = 5 - 3i, z_{2} = i + 2}
$