Disciplined convex programming information:
exp(X) is convex and nondecreasing in X. When used in CVX
expressions, X must be real. Typically, X must also be affine
or convex; X can also be concave, but this produces a log-concave
result with very limited usefulness.
You’ll have to deal separately with the real and imaginary parts. And deal with each of these in accordance with CVX;s rules. If it’s even possible to do so and end up with convex (or concave) expressions.
So until you show usage to the contrary, let’s just say it is non-convex.