Question

Real part of $e^{e^{i\theta }}$ is

• A. $e^{\cos \theta }\left[\cos \right(\sin \theta \left)\right]$
• B. $e^{\cos \theta }\left[\cos \right(\cos \theta \left)\right]$
• C. $e^{\sin \theta }\left[\sin \right(\cos \theta \left)\right]$
• D. $e^{\sin \theta }\left[\sin \right(\sin \theta \left)\right]$

Answer 1

The correct option is A $e^{\cos \theta }\left[\cos \right(\sin \theta \left)\right]$

$e^{e^{i\theta }}=e^{\cos \theta +i\sin \theta }=e^{\cos \theta }\left(e^{i\sin \theta }\right)$

$\therefore e^{\cos \theta }\left(e^{i\sin \theta }\right)=e^{\cos \theta }\left(\cos \sin \theta \right)+i{e}^{\cos \theta }\left(\sin \sin \theta \right)$

$\therefore$ The real part is $e^{\cos \theta }\left(\cos \sin \theta \right)$