Euler's equation demonstrates the relationship between e and the trigonometric functions. The equation is stated as follows:

     e^ix = cos(x) + i*sin(x)

     This can easily be shown to be true by replacing cos(x) and sin(x) with their respective formulations and simplifying.

     sin(x) = (e^xi - e^-xi)/2i
     cos(x) = (e^xi + e^-xi)/2
     e^ix = (e^xi + e^-xi)/2 + i*(e^xi - e^-xi)/2i
     e^ix = (e^xi + e^-xi)/2 + (e^xi - e^-xi)/2
     e^ix = (e^xi + e^xi)/2
     e^ix = 2e^xi/2
     e^ix = e^xi

What's It Good For?

eix	Calculating ln(i)

More Resources

Euler's Equation Explained By Dr. Math