1. ## Complex conjugate

Suppose z e C (z is an element of the complex numbers)

Let z = x + yi with x,y e R.

Let (z) = x - yi with x,y e R.

Prove: (z) = z if and only if z is a real number.

I'm having trouble with this proof in both directions. Thanks for any help.

2. Originally Posted by jzellt
Suppose z e C (z is an element of the complex numbers)

Let z = x + yi with x,y e R.

Let (z) = x - yi with x,y e R.

Prove: (z) = z if and only if z is a real number.

I'm having trouble with this proof in both directions. Thanks for any help.
If z is real then y = 0 and it is trivially seen that z = (z).

If (z) = z then x = x and y = -y => y = 0 => z is real.