Euler showed that given a complex number $a+bi$ there are real number $r$ and $\theta$ such that:
 The transcendental number $e$ is also named after Euler.

• $a+bi=re^{i\theta}$
This is the so-called polar representation of a complex number.

The value $r$ is the magnitude of a complex number and is calculated using Pythagoras' Theorem as:

• $r~=~\sqrt{a^2+b^2}$
Using this representation we get the identity:

• $a+bi~=~r(\cos(\theta)+i\sin(\theta))$

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