Question

(a+ib)/(c+id)=x+iy prove that (a-ib)/(c-id)=x-iy​

Answer 1

Rules :

Before we solve this problem, we must know some important properties on Complex Numbers.

1. If z = a + ib, be a complex number, then its conjugate be

Conjugate of z = a - ib

2. Conjugate of (z₁ / z₂)

= conjugate of z₁ / conjugate of z₂

Solution :

Given,

(a + ib) / (c + id) = x + iy

Taking conjugate in both sides, we get

Conjugate of {(a + ib) / (c + id)}

= Conjugate of (x + iy)

or, {conjugate of (a + ib)} / {conjugate of (c + id)} = x - iy, (by 1 & 2)

or, (a - ib) / (c - id) = x - iy (by 1)

Hence, proved.