If u+iv=3ix+iy+2 , then y in terms of u,v is

x+iy=3iu+iv-2=-2u+i3-2vu+iv=-2u+i3-2vu-ivu2+v2comparing imaginary part, y=3uu2+v2

x+iy=3iu+iv-2=-2u+i3-2vu+iv=-2u+i3-2vu-ivu2+v2comparing imaginary part, y=3uu2+v2

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If $u + i v = \frac{3 i}{x + i y + 2}$ , then y in terms of u,v is

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$\frac{5 u}{u^{2} + v^{2}}$

$\frac{2 u}{u^{2} + v^{2}}$

$\frac{3 u}{u^{2} + v^{2}}$

$\frac{4 u}{u^{2} + v^{2}}$

answer is A.

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$x + i y = \frac{3 i}{u + i v} - 2 = \frac{[- 2 u + i (3 - 2 v)]}{u + i v} = \frac{[- 2 u + i (3 - 2 v)] (u - i v)}{u^{2} + v^{2}}$

comparing imaginary part, $y = \frac{3 u}{u^{2} + v^{2}}$

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