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  4. If z=2-3 i, then value of z2-4 z+13 is

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Q. If $z=2-3 i$, then value of $z^{2}-4 z+13$ is

Complex Numbers and Quadratic Equations

Solution:

We have, $z=2-3 i$
$\Rightarrow z-2=-3 i $
$\Rightarrow (z-2)^{2}=(-3 i)^{2}$
$\Rightarrow z^{2}-4 z+4=9 i^{2}$
$ \Rightarrow z^{2}-4 z+13=0$