Real part of e e i θ is Options: A . &nbspecosθ [cos(sinθ)] B . &nbspecosθ [cos(cosθ)] C . &nbspesinθ [cos(sinθ)] D . &nbspesinθ [sin(sinθ)]

Real part of eeiθ is

Question

Real part of

e^{e^{i θ}}

Options:

A . ecosθ [cos(sinθ)]

B . ecosθ [cos(cosθ)]

C . esinθ [cos(sinθ)]

D . esinθ [sin(sinθ)]

Answer: Option A
:
A

e^{e^{i θ}} = e^{c o s θ + i s i n θ} = e^{c o s θ} e^{i s i n θ} = e^{c o s θ} [c o s (s i n θ) + i s i n (s i n θ)] ∴ R e a l p a r t o f e^{e^{i θ}} i s e^{c o s θ} [c o s (s i n θ)]

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