Question

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

Answer 1

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

$e^{ei\theta }=e^{cis\theta }=e^{\cos \theta +isin\theta }$

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

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

Hence, the real part is

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