Question

For $x+iy=\sqrt{\frac{a+ib}{c+id}}$ then find the value of $x^2+y^2$.

Answer 1

Given,

$x+iy=\sqrt{\frac{a+ib}{c+id}}$

Now squaring both sides we get,

$(x+iy{)}^2=\frac{a+ib}{c+id}$

Now taking modulus both sides we get,

$|(x+iy{)}^2|=\left|\frac{a+ib}{c+id}\right|$

or, $x^2+y^2=\frac{a^2+b^2}{c^2+d^2}$.