Exponential form

Every complex number z is the sum of a real and an imaginary component, z=a+bi. If you consider complex numbers to be coordinates in the complex plane with the x-axis consisting of real numbers and the y-axis pure imaginary numbers, then every point z=a+bi can be graphed as (x,y)=(a,b). We can convert z into polar form and re-write it as , where r=|z|. By Euler's formula, which states that , we can conveniently (yes, again!) rewrite z as , which is the general exponential form of a complex number.