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## Homework Statement

I know following that [tex]|z| = 1[/tex] where [tex] z \in \mathbb{C}[/tex] is the definition of unit circle in the complex plane.

then if the exist another complex number c which lies within the distance r from z then distance from the two numbers kan be discribe as

|z-c| = r

If two questions here.

Since both z and c lies within the complex plane is the distance r also a complex number?

Can I conclude that |z-c| = r is a line within the complex plane?

Sincerely

Susanne

p.s. if I square this both sides

[tex]|z-c|^2 = r^2[/tex] then its a circle in the complex plane?

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