So, I was reading my Math 405 (A Math Teacher's Course) Book for class the other day, and I noticed that while I was studying complex numbers, the term number theory jumped up at me. I thought I would share how number theory was connected to my Math 405 class with all of you!

I was reading about the history of Complex Numbers, and my book said that, "In the 1700s, Euler used complex numbers to derive some new results in number theory." After reading this, I wanted to know what new results they were talking about and here is what I found from wikipedia:

Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that shows a deep relationship between the trigonometric functions and the complex exponential function. Euler's formula states that, for any real number x,

e^{ix} = \cos x + i\sin x \!

where e is the base of the natural logarithm, i is the imaginary unit, and cos and sin are the trigonometric functions cosine and sine, with the argument x given in radians. The formula is still valid if x is a complex number, and so some authors refer to the more general complex version as Euler's formula.[1]

Richard Feynman called Euler's formula "our jewel" and "the most remarkable formula in mathematics".[2]

I thought it was interesting how someone called this formula the most remarkable formula in math! Wow!