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Summation by Sigma Method

If z=2-3i t...

Question

If $z = 2 - 3 i$ then $z^{2} - 4 z + 13 =$

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Solution

The correct option is A $0$
$z = 2 - 3 i$
$z^{2} = 2^{2} - 3^{2} - 12 i$
$= - 5 - 12 i$
$∴ z^{2} - 4 z + 13$
$= (- 5 - 12 i) - 4 (2 - 3 i) + 13$
$= - 5 - 12 i - 8 + 12 i + 13$
$= - 13 + 13$
$= 0$

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