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If $x+iy=\sqrt{\large\frac{a+ib}{c+id}}$,then the value of $\large\frac{(x^2+y^2)^2(c^2+d^2)}{(a^2+b^2)}$ is

$\begin{array}{1 1}(A)\;x^2+y^2&(B)\;(x^2+y^2)^2\\(C)\;1&(D)\;0\end{array} $

1 Answer

$(x+iy)^2=\large\frac{a+ib}{c+id}$
$|(x+iy)^2|=|\large\frac{a+ib}{c+id}\mid$
$\Rightarrow |x+iy|^2=|\large\frac{a+ib}{c+id}\mid$
$\Rightarrow x^2+y^2=\large\frac{\sqrt{a^2+b^2}}{\sqrt{c^2+d^2}}$
$\Rightarrow (x^2+y^2)^2\large\frac{(c^2+d^2)}{(a^2+b^2)}$$=1$
Hence (C) is the correct answer.
answered Apr 10, 2014 by sreemathi.v
 
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