Every complex number is the sum of a real and an imaginary component, . If you consider complex numbers to be coordinates in the complex plane with the -axis consisting of real numbers and the -axis pure imaginary numbers, then any point can be plotted at the point as . We can convert into polar form and re-write it as , where . By Euler's formula, which states that , we can conveniently (yes, again!) rewrite as , which is the general exponential form of a complex number.
So looks like:
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