Equation of Circle in Complex Plane/Examples/Radius 4, Center (0, 0)

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Example of Use of Equation of Circle in Complex Plane

The equation:

$z \overline z = 16$

describes a circle embedded in the complex plane whose center is at $\tuple {0, 0}$ and whose radius is $4$.


Proof

\(\ds z \overline z\) \(=\) \(\ds 16\)
\(\ds \leadsto \ \ \) \(\ds \paren {x + i y} \paren {x - i y}\) \(=\) \(\ds 16\)
\(\ds \leadsto \ \ \) \(\ds x^2 + y^2\) \(=\) \(\ds 16\)

The result follows from Equation of Circle in Cartesian Plane.

$\blacksquare$


Sources