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

Complex Numbers and Quadratic Equations

Solution:

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