Question and Answers Forum

All Questions      Topic List

Vector Calculus Questions

Previous in All Question      Next in All Question      

Previous in Vector Calculus      Next in Vector Calculus      

Question Number 5153 by 1771727373 last updated on 23/Apr/16

$$proof{e}^{i\mathrm{\Theta }}=cos\left(\mathrm{\Theta }\right)+isin\left(\mathrm{\Theta }\right)$$

Answered by 123456 last updated on 23/Apr/16

$$\mathrm{lets}f\left(\theta \right)=\cos \theta +i\sin \theta ,f\left(0\right)=1$$$$\frac{\partial f}{\partial \theta }=-\sin \theta +i\cos \theta =i(\cos \theta +i\sin \theta )=if$$$$\frac{df}{f}=id\theta$$$$\ln f=i\theta +k$$$$f=e^{i\theta +k}=e^{i\theta }{e}^k={ce}^{i\theta }$$$$f\left(0\right)=1\Rightarrow {ce}^0=c=1$$$$f\left(\theta \right)=e^{i\theta }$$$$$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com