Question

If $x+iy=\sqrt{\left[\frac{a-ib}{c-id}\right]}$, then $(x^2+y^2{)}^2=$?

Answer 1

Given $x+iy=\sqrt{\left[\frac{a-ib}{c-id}\right]}$

Applying modulus on both sides

$|x+iy|=\sqrt{\left[|\frac{a-ib}{c-id}|\right]}=\sqrt{\frac{|a-ib|}{|c-id|}}$

$⟹\sqrt{x^2+y^2}=\sqrt{\frac{\sqrt{a^2+b^2}}{\sqrt{c^2+d^2}}}$

$⟹(x^2+y^2{)}^2=\frac{a^2+b^2}{c^2+d^2}$