Mathematics - Complex Number Question with Solution | TestHub

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

so ${\alpha }^2=-2i+1={\beta }^2$

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

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

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

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