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

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4-1.Complex numbers

medium

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

$x = 0.5\,\,,\,\,y = 3.5$

$x = 5\,\,,\,\,y = 3$

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

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

Solution

(a) $3 – 2yi = {9^x} – 7i$
Equating real and imaginary parts both sides
${9^x} = 3 \Rightarrow \,{3^{2x}} = {3^1} \Rightarrow 2x = 1 \Rightarrow x = 0.5$
$2y = 7 \Rightarrow \,y = 3.5$.

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