Question

The value of $e^{2+i}$ is

• A. $e[\cos 1+i\sin 1]$
• B. $e^2[\cos 1+i\sin 1]$
• C. $\cos 1+i\sin 1$
• D. $e^{-2}[\cos 1+i\sin 1]$

Answer 1

The correct option is B $e^2[\cos 1+i\sin 1]$

We have, $e^{i\theta }=\cos \theta +i\sin \theta$
$\Rightarrow e^{2+i}=e^2\cdot e^i=e^2(\cos 1+i\sin 1)$