If $i^{2} = - 1$ , then $(5 + 6 i)^{2} =$

- 11

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- 11 + 11 i

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- 11 + 30 i

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- 11 + 60 i

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61

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Solution

The correct option is D $- 11 + 60 i$
We know $(a + b)^{2} = a^{2} + 2 a b + b^{2}$
$∴ (5 + 6 i)^{2} = 5^{2} + 2 \times 5 \times 6 i + 36 i^{2}$
As $i^{2} = - 1$
$\Rightarrow 25 + 60 i + 36 (- 1)$
$\Rightarrow 25 + 60 i - 36$
$\Rightarrow - 11 + 60 i$

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