Repicrocal of a complex number

Definition

Let $z\in C$ st. $z{\ne }_0$. Then,

\frac{1}{z} = \frac{\bar{z}}{|z|^2}

Remember the modulus is $\sqrt{z\bar{z}}$. Then,

$$\frac{1}{z}=\frac{\bar{z}}{|z{|}^2}=\frac{\bar{z}}{z\bar{z}}$$

Also the division is possible

$$\frac{z_1}{z_2}=z_1\frac{1}{z_2}=\frac{z_1\overline{z_2}}{|z_2{|}^2}$$