If $ x+iy = \sqrt{\frac{a+ib}{c+id} } ,$Show that$ (x^2+y^2)^2 = \frac {a^2+b^2}{c^2+d^2} $ $ x+iy = \sqrt{\frac{a+ib}{c+id} } , $Show that $ ({x^2+y^2})^2 = \frac {a^2+b^2}{c^2+d^2} $
How do i do this ?I tried squaring both sides but x+iy expansion becomes difficult when squaring the next time .I also tried conjugating the R.H.S

$$x^2+y^2=|x+iy|^2=\left|\sqrt{\frac{a+ib}{c+id}}\right|^2=\left|\frac{a+ib}{c+id}\right|$$
Therefore,
$$(x^2+y^2)^2=\frac{|a+ib|^2}{|c+id|^2}=\frac{a^2+b^2}{c^2+d^2}$$
