If $(x + i y)^{2} = 7 + 24 i,$ then $y^{2}$ is equal to

16

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9

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25

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12

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Solution

The correct option is B $9$
Consider the given complex number.
$(x + i y)^{2} = 7 + 24 i$
$x^{2} + i^{2} y^{2} + 2 x y i = 7 + 24 i$
$x^{2} - y^{2} + 2 x y i = 7 + 24 i$

On comparing real part and imaginary part, we get
$x^{2} - y^{2} = 7$ $. . . . . . . (1)$
$2 x y = 24$
$x y = 12$ $. . . . . . . (2)$

On solving equation $(1)$ and $(2)$ , we get
$y^{2} = 9$

Hence, this is the answer.

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