Question

If $z(2-i)=(3+i)$, then $z^{20}$ is equal to

• A. $2^{10}$
• B. $-2^{10}$
• C. $2^{20}$
• D. $-2^{20}$

Answer 1

Answer: (B)

We have, $z\left(2-i\right)=\left(3+i\right)$
$\Rightarrow z=\left(\frac{3+i}{2-i}\right)\times \left(\frac{2+i}{2+i}\right)$
$=\frac{5+5i}{5}$
$\Rightarrow z=1+i$
$\Rightarrow z^2=2i$
$\Rightarrow z^{20}$
$=-2^{10}$