Exponential form
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:
See also
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