Students will learn what Euler's formula is and see the proof of Euler's formula that doesn't require Taylore series. Students will also see a corollary of Euler's formula called Euler's identity, which is often referred to as the most beautiful equation. Here's a proof of both Euler's formula and identity. Students will also learn how to use Euler's formula to convert complex numbers to exponential form. For example, convert \(-1 + \sqrt{3}i\) to exponential form. As another example, convert the following to exponential form:

$$\sqrt{2}\left(\cos \dfrac{3\pi}{4} + i\sin \dfrac{3\pi}{4}\right)$$