Complex Numbers And Quadratic Equations question 835
Question: Real part of $ {e^{{e^{i\theta }}}} $ is [RPET 1995]
Options:
A) $ {e^{\cos \theta }}[\cos (\sin \theta )] $
B) $ {e^{\cos \theta }}[\cos (\cos \theta )] $
C) $ {e^{\sin \theta }}[\sin (\cos \theta )] $
D) $ {e^{\sin \theta }}[\sin (\sin \theta )] $
Show Answer
Answer:
Correct Answer: A
Solution:
$ {e^{{e^{i\theta }}={e^{\cos \theta +i\sin \theta }}={e^{\cos \theta }}[{e^{i\sin \theta }}]}} $ $ ={e^{\cos \theta }}[\cos (\sin \theta )+i\sin (\sin \theta )] $ \ Real part of $ {e^{{e^{i\theta }}}} $ is $ {e^{\cos \theta }}[\cos (\sin \theta )] $
BETA
