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Susanne217
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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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