Which of the following is the exponential form of a complex number?

The exponential form of a complex number $z$ is given by Euler's formula, which relates the polar form to the exponential form.

A complex number can be written in:

• Rectangular form: $z = a + ib$
• Polar form: $z = r(\cos \theta + i \sin \theta)$, where $r$ is the modulus and $\theta$ is the argument.
• Exponential form: $z = re^{i\theta}$

Comparing this with the given options:
(A) $e^{x+x+x^2/2!}$ is not the standard exponential form.
(B) $e^x$ is a real exponential function.
(C) $re^{i\theta}$ is the correct exponential form of a complex number.
(D) $a+ib$ is the rectangular form of a complex number.

The correct option is (C).

The final answer is $\boxed{\text{C}}$