# 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. $\overline{r e^{i \phi}} = r e^{-i \phi}$.