# Equation of Unit Circle in Complex Plane/Corollary 2

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## 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:

- $\overline z = \dfrac 1 z$

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

## Proof

From Equation of Unit Circle in Complex Plane: Corollary 1, the equation of $C$ can also be given by:

- $z \overline z = 1$

The result follows by multiplying by $\dfrac 1 z$.

$\blacksquare$

## Sources

- 1960: Walter Ledermann:
*Complex Numbers*... (previous) ... (next): $\S 3$. Roots of Unity