A) \[{{e}^{r\sin \theta }}\]
B) \[{{e}^{-r\sin \theta }}\]
C) \[{{e}^{-r\cos \theta }}\]
D) \[{{e}^{r\cos \theta }}\]
Correct Answer: B
Solution :
If \[z=r{{e}^{i\theta }}=r(\cos \theta +i\sin \theta )\] Þ \[iz=ir(\cos \theta +i\sin \theta )=-r\sin \theta +ir\cos \theta \] or \[{{e}^{iz}}={{e}^{(-r\sin \theta +ir\cos \theta )}}={{e}^{-\sin \theta }}{{e}^{ri\cos \theta }}\] or \[|{{e}^{iz}}|=|{{e}^{-r\sin \theta }}||{{e}^{ri\cos \theta }}|\]\[={{e}^{-r\sin \theta }}|{{e}^{ir\,\cos \theta }}|\] \[={{e}^{-r\sin \theta }}{{[\{{{\cos }^{2}}(r\cos \theta )+{{\sin }^{2}}(r\cos \theta )\}]}^{1/2}}={{e}^{-r\sin \theta }}\]
You need to login to perform this action.
You will be redirected in
3 sec
