Euler’s Formula: A Complete Guide

In the world of complex numbers, as we integrate trigonometric expressions, we will likely encounter the so-called Euler’s formula.

Named after the legendary mathematician Leonhard Euler, this powerful equation deserves a closer examination — in order for us to use it to its full potential.

We will take a look at how Euler’s formula allows us to express complex numbers as exponentials, and explore the different ways it can be established with relative ease.

In addition, we will also consider its several applications such as the particular case of Euler’s identity, the exponential form of complex numbers, alternate definitions of key functions, and alternate proofs of de Moivre’s theorem and trigonometric additive identities.

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