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Complex Numbers

If z =-5+2√...

Question

If $z = - 5 + 2 \sqrt{- 4}$ , then the value of $z^{2} + 10 z + 41$ is equal to

A

2

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B

-2

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C

0

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D

None of these

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Solution

The correct option is B 0
$z = - 5 + 4 i$
$z + 5 = 4 i$
Squaring on both sides
$z^{2} + 10 z + 25 = - 16$
$z^{2} + 10 z + 41 = 0$

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