Question

The period of $e^z$ is

• A. $2\mathrm{\pi }$
• B. $\mathrm{\pi }$
• C. $2\mathrm{\pi i}$
• D. $\mathrm{\pi i}$

Answer 1

The correct option is C

$2\mathrm{\pi i}$

Define the period of an exponential function

1. When a function repeats its values at regular intervals or periods is known as a periodic function.
2. The particular interval after which a function repeats its values is called the period of the function.
3. The graph of an exponential function is given along.
4. The graph depicts that an exponential function is periodic and have a purely imaginary period $2\mathrm{\pi i}$.

Thus, the period of the exponential function $e^z$ is $2\mathrm{\pi i}$ which is imaginary.

Hence, option (C) is the correct option.