Let α and β be the roots of the equation x ^ 2 + (2i - 1) = 0 ....

Since $\alpha$ and $\beta$ are the roots of the equation ${x}^{2} + 2i - 1 = 0$

so ${\alpha}^{2} = - 2i + 1 = {\beta}^{2}$

$⇒ {\alpha}^{4} = {\left(- 2i + 1\right)}^{2} = 4{i}^{2} + 1 - 4i = - 3 - 4i$

$⇒ {\alpha}^{8} = {\left(- 3 - 4i\right)}^{2} = - 7 + 24i$

Similarly, ${\beta}^{8} = - 7 + 24i$

$∴ \left|{\alpha}^{8} + {\beta}^{8}\right| = \left|- 14 + 48i\right| = 50$