# Thread: Defining a unit circle.

1. ## 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 $2 \pi$ and one centred at $2 \pi i$.

2. ## Re: Defining a unit circle.

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.

3. ## Re: Defining a unit circle.

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 $2 \pi$ and one centred at $2 \pi i$.
Recall that for complex numbers $z~\&~w$ the $|z-w|$ is the distance between them.

Informally we can write $|z-2\pi|=1~\&~|z-2\pi i|=1$.

More formally $\{z:~|z-2\pi i|=1\}$, the set of numbers a distance of 1 from $2\pi i$.