Complex Conjugate and Modulus

The complex conjugate of a complex number $z = a +bi$, which we denote either by $\bar{z}$ or $z^{*}$, is defined as:

$$\bar{z} = a - bi$$

i.e. we just flip the sign of the imaginary part of $z$.

Visually, taking the complex conjugate amounts to reflecting $z$ across the real axis. For example:

...