Translations:Appendix D: Exercises/7/en

3. Show that Euler’s equation $e^{i\theta }{\rm {=\ cos\ }}\theta {\ +\ }i{\rm {\ sin\ }}\theta$ for $\theta {\ =\ }\pi$ gives $e^{i\pi }{\ =\ }-{\rm {1}}$. This equation is considered to be one of the most beautiful equations in mathematics because it relates the four special numbers $e,\;i,\;\pi ,\;-1$ to each other.