Equation of Circle in Complex Plane/Formulation 1/Exterior

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Theorem

Let $\C$ be the complex plane.

Let $C$ be a circle in $\C$ whose radius is $r \in \R_{>0}$ and whose center is $\alpha \in \C$.


The points in $\C$ which correspond to the exterior of $C$ can be defined by:

$\left\lvert{z - \alpha}\right\rvert > r$

where $\left\lvert{\, \cdot \,}\right\rvert$ denotes complex modulus.


Proof

From Equation of Circle in Complex Plane, the circle $C$ itself is given by:

$\left\lvert{z - \alpha}\right\rvert = r$



Sources