Question

Is {e^x} periodic function?

Answer 1

no. Because , if it had a period, say k > 0, then that would mean that

e^(x+k) = e^x
e^x e^k = e^x
e^k = 1
k=0

But, we specified k > 0.

I mean, just look at the graph. Surely it is not periodic!

Now, if we use a complex number z, then it is true that e^z is periodic.