Question

$e^z$ is a periodic with a period of

• A. $2\pi$
• B. $2\pi i$
• C. $\pi$
• D. $i\pi$

Answer 1

The correct option is B $2\pi i$

$f\left(z\right)=e^z$
$f(z+T)=e^{z+T}=e^z.e^T$
For a periodic function
$f(z+T)=f\left(z\right)$
$\Rightarrow e^T=1=cos2n\pi +isin2n\pi$
for $n=1$
$e^T=cos2\pi +isin2\pi =e^{i2\pi }$
$\therefore$Period of $f\left(z\right)=i2\pi$