Equation of Unit Circle in Complex Plane/Corollary 1

Corollary to Equation of Unit Circle in Complex Plane
Consider the unit circle $C$ whose center is at $\left({0, 0}\right)$ on the complex plane.

The equation of $C$ can be given by:
 * $z \overline z = 1$

where $\overline z$ denotes the complex conjugate of $z$.

Proof
From Equation of Unit Circle in Complex Plane, the equation of $C$ can also be given by:


 * $\cmod z = 1$

where $\cmod z$ denotes the complex modulus of $z$.

Thus: