Equation of Unit Circle in Complex Plane/Proof 1

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Theorem

Consider the unit circle $C$ whose center is at $\tuple {0, 0}$ on the complex plane.

Its equation is given by:

$\cmod z = 1$

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


Proof

From Equation of Unit Circle, the unit circle whose center is at the origin of the Cartesian $xy$ coordinate plane has the equation:

$x^2 + y^2 = 1$

Identifying the Cartesian $xy$ coordinate plane with the complex plane: