Equation of Unit Circle in Complex Plane/Corollary 2

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