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Solving $3 - 2 y i = 9^{x} - 7 i$ , where $i^{2} = - 1,$ for x and y real, we get

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$x = 0, y = \frac{3 + 7 i}{2 i}$

$x = \frac{1}{2}, y = 7$

$x = 5, y = 3$

$x = 0.5, y = 3.5$

answer is A.

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Detailed Solution

$3 - 2 y i = 9^{x} - 7 i$

Equating real and imaginary parts both sides

$9^{x} = 3 \Rightarrow 3^{2 x} = 3^{1} \Rightarrow 2 x = 1 \Rightarrow x = 0.5$

$2 y = 7 \Rightarrow y = 3.5 .$

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