If x + yi = √ ((a + ib)/(c + id)), prove that (x^2 + y^2)^2 = (a^2 + b^2)/(c^2 + d^2)

Question

If x + yi = \(\sqrt{\frac{a+ib}{c+id}}\)

√ ((a + ib)/(c + id)), prove that

(x² + y²)² = \(\frac{a^2 + b^2}{c^2+d^2}\)

(a² + b²)/(c² + d²)

Answer 1

x + iy = \(\sqrt{\frac{a+ib}{c+id}}\)

Equating real and imaginary parts, we get