Question

Let $\alpha$ and $\beta$ be the roots of the equation $x^2+(2i-1)=0$. Then, the value of $\left|{\alpha }^8+{\beta }^8\right|$ is equal to :

• A. 50
• B. 250
• C. 1250
• D. 1500

Answer 1

Answer: (A)

$X^2=1-2i\Rightarrow {\alpha }^2=1-2i,{\beta }^2=1-2i$
Hence ${\alpha }^8={\beta }^8$
$\left|{\alpha }^8+{\beta }^8\right|=\left|2{\alpha }^8\right|=2{\left|{\alpha }^2\right|}^4$
$=2{\sqrt{5}}^4=50$