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.

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:

Using this representation we get the identity:

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Polar Representation Of A Complex Number