If Z = 3 - 4i, then the value of expression $z^{4} - 3 z^{3} + 3 z^{2} + 99 z - 95$ is equal to

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Detailed Solution

$z = 3 - 4 i$
$z - 3 = - 4 i \Rightarrow {(z - 3)}^{2} = {(- 4 i)}^{2} \Rightarrow z^{2} - 6 z + 9 = - 16$
$\Rightarrow z^{2} - 6 z + 25 = 0 \Rightarrow z^{4} - 3 z^{3} + 3 z^{2} + 99 z - 95 = (z^{2} + 3 z - 4) (z^{2} - 6 z + 25) + 5 = 5$

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