if e gets in power of (tetta*i) makes a rotating circle in complex plan

[im alex]

I have a question
I know if e gets in power of (tetta*i) makes a rotating circle in complex plan
But what if a whole number 2 like get in power of a comlex number (2^3i for example)
And what does it mean ??
And what shape will form if we plot somthing like this C*A^(a+bi)
C ,A : constant

 

[tkhunny]

\(\displaystyle 2^{x} = e^{x\ln(2)}\)

 

[im alex]

\(\displaystyle 2^{x} = e^{x\ln(2)}\)

Thank you tkhunny
god i must plot this