Euler's Formula/Proof

Theorem

 * $e^{i \theta} = \cos \theta + i \sin \theta$

where $e^\cdot$ is the complex exponential function, $\cos$ is cosine, $\sin$ is sine, and $i$ is the imaginary unit.

Thus we define the complex exponential function in terms of standard trigonometric functions.

Direct Proof 3
As Sine Function is Absolutely Convergent and Cosine Function is Absolutely Convergent, we have: