​ If x + iy = a+ib/a - ib, prove that x^2 + y^2 = 1. ​

Question

If x + iy \(=\frac{a+ib}{a-ib}\), prove that x² + y² = 1.

Answer 1

Consider the given equation,

 x + iy \(=\frac{a+ib}{a-ib}\) 

Now, rationalizing

On comparing both the sides, we get

Now, we have to prove that x² + y² = 1

Taking LHS,

x² + y²

Putting the value of x and y, we get