Question

If $x+iy=\sqrt{\frac{a+ib}{c+id}}$, prove that $(x^{2}+y^{2})^{2}=\frac{a^{2}+b^{2}}{c^{2}+d^{2}}$

Answer 1

Answer:

Step-by-step explanation:

Hi,

Given that x + iy = √(a+ib)/(c +id)----(1)

To get a conjugate  of complex number simply, we need to

replace i in every term by -i

Conjugate of x + iy is x - iy

x - iy = √(a-ib)/(c -id)------(2)

Multiplying (1) and (2), we get

(x + iy)*(x - iy) = √(a + ib)/(c + id)*√(a - ib)/(c - id)

(x² - (iy)²) = √(a² - (ib)²/c² - (id)²

x² + y² = √(a² + b²/c² + d²)

Squaring on both sides, we get

x² + y² = a² + b²/c² + d²

Hope, it helps !