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 $\displaystyle 2 \pi $ and one centred at $\displaystyle 2 \pi i $.
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 $\displaystyle 2 \pi $ and one centred at $\displaystyle 2 \pi i $.
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.
Recall that for complex numbers $\displaystyle z~\&~w$ the $\displaystyle |z-w|$ is the distance between them.
Informally we can write $\displaystyle |z-2\pi|=1~\&~|z-2\pi i|=1$.
More formally $\displaystyle \{z:~|z-2\pi i|=1\}$, the set of numbers a distance of 1 from $\displaystyle 2\pi i$.