Thread: Defining a unit circle.

Here's an easy one for someone.

How do I define a unit circle in the complex plane that's not centred at the origin, specifically I need to define one centred at and one centred at .

Hey rushton.

The circle in complex numbers is defined by |z| = R. But if you shift z by some constant, how will that affect where the circle is?

Hint: Recall that in normal real number math, (x-a)^2 + (y-b)^2 = R^2 is centred at (a,b) with a radius of R.

Originally Posted by rushton

How do I define a unit circle in the complex plane that's not centred at the origin, specifically I need to define one centred at and one centred at .

Recall that for complex numbers the is the distance between them.

Informally we can write .

More formally , the set of numbers a distance of 1 from .