5 - Interesting properties of the absolute value of complex numbers

An immediate realization is that any complex number , , etc... will have the same modulus, so, they are related by:
And well, this equation really seems familiar, huh?

The equation above is a form of the circle equation.
The modulus of a complex number, as we said, is the distance from the origin. So, for a circle, this is the radius of that circle.