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Complex Numbers

If z=-1+3i ...

Question

If $z = - 1 + 3 i$ then $z^{2} + 2 z + 10 =$

A

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Solution

The correct option is A $0$
$z^{2} + 2 z + 10$
$= (z + 1)^{2} + 10 - 1$
$= (z + 1)^{2} + 9$
$= (- 1 + 3 i + 1)^{2} + 9$
$= (3 i)^{2} + 9$
$= - 9 + 9$
$= 0$
Hence, $z^{2} + 2 z + 10 = 0$ where $z = - 1 + 3 i$ .

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