Real part of e e i θ is Options: A . &nbsp e c o s θ [cos(sin θ )] B . &nbsp e c o s θ [cos(cos θ )] C . &nbsp e s i n θ [cos(sin θ )] D . &nbsp e s i n θ [sin(sin θ )]

Real part of eeiθ is

Discussion Forum : Complex Numbers

Question -

Real part of $e^{e^{i θ}}$ is

Options:

A .

e^{c o s θ}

[cos(sin

θ

)]

B .

e^{c o s θ}

[cos(cos

θ

)]

C .

e^{s i n θ}

[cos(sin

θ

)]

D .

e^{s i n θ}

[sin(sin

θ

)]

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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