## Abstract

For many mathematicians, a certain characteristic about an area of mathematics will lure him/her to study that area further. That characteristic might be an interesting conclusion, an intricate implication, or an appreciation of the impact that the area has upon mathematics. The particular area that we will be exploring is Euler's Formula, $e^{ix}=\cos{x}+i\sin{x}$, and as a result, Euler's Identity, $e^{i\pi}+1=0$. Throughout this paper, we will develop an appreciation for Euler's Formula as it combines the seemingly unrelated exponential functions, imaginary numbers, and trigonometric functions into a single formula. To appreciate and further understand Euler's Formula, we will give attention to the individual aspects of the formula, and develop the necessary tools to prove it. We will also try to gain a small understanding of the impact that it has had on mathematics.

## Faculty Sponsor

Ryan Zerr

## Recommended Citation

Larson, Caleb
(2017)
"An Appreciation of Euler's Formula,"
*Rose-Hulman Undergraduate Mathematics Journal*: Vol. 18:
Iss.
1, Article 17.

Available at:
https://scholar.rose-hulman.edu/rhumj/vol18/iss1/17