Question

Prove the following properties:

z is real if and only if z = `bar(z)`

Answer 1

z is real if z = `bar(z)`

Let z = x + iy

z = `bar(z)`

⇒ x + iy = x – iy

⇒ 2iy = 0

⇒ y = 0

⇒ z is real.

Z is real if z = `bar(z)`