ACIT4330-Page/content/Definitions/Complex Analysis/Complex Conjugation.md

Definition

Let z = x + iy. Then its complex conjugate is

\bar{z} := x-iy.

Properties

The following hold:

1. \mid z \mid^2 = z \bar{z},
2. z + \bar{z} = 2 \mathrm{Re} z,
3. z - \bar{z} = 2i \mathrm{Im} z,
4. \overline{r e^{i \phi}} = r e^{-i \phi}.