Appendix A - Review of Complex Numbers - Exercises for A - Problems - Page 796: 23

Proof of formula

To Prove That:- $\;\;e^{iπ}+1=0$ We will use the Euler's Formula \[e^{i\theta}=\cos\theta+i\sin\theta\] Consider $e^{iπ}$ By using Euler's Formula \[e^{iπ}=\cos π+i\sin π\] \[e^{iπ}=-1+i(0)\] \[e^{iπ}=-1\] \[e^{iπ}+1=0\] Hence prove.