If u+iv = frac{3i}{x+iy+2},then y= | vedclass

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(B) Given,$u+iv = \frac{3i}{(x+2)+iy}$.Taking the reciprocal on both sides:$\frac{1}{u+iv} = \frac{(x+2)+iy}{3i}$.Multiply the numerator and denominat

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

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(B) Given,$u+iv = \frac{3i}{(x+2)+iy}$.Taking the reciprocal on both sides:$\frac{1}{u+iv} = \frac{(x+2)+iy}{3i}$.Multiply the numerator and denominator of the left side by the conjugate $(u-iv)$:$\frac{u-iv}{u^2+v^2} = \frac{(x+2)+iy}{3i}$.Multiply both sides by $3i$:$(x+2)+iy = \frac{3i(u-iv)}{u^2+v^2} = \frac{3ui - 3vi^2}{u^2+v^2} = \frac{3v + 3ui}{u^2+v^2}$.Equating the imaginary parts:$y = \frac{3u}{u^2+v^2}$.

If $u+iv = \frac{3i}{x+iy+2}$,then $y=$

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