What is the product of the complex numbers $(- 3 i + 4)$ and $(3 i + 4)$ ?

1

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7

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25

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- 7 + 24 i

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7 + 24 i

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Solution

The correct option is C $25$
Consider the product of the complex numbers as shown below:
$(- 3 i + 4) (3 i + 4) = (- 3 i) (3 i) - 3 i (4) + 4 (3 i) + 4 (4)$
$= - 9 i^{2} - 12 i + 12 i + 16$
$= - 9 (- 1) + 16 = 9 + 16$
$= 25$
Hence, option C is the correct answer.

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