Can we somehow calculate $a^z$ where z is a complex number ?
Does normal exponent rules like :
$$a^b\cdot a^c=a^{b+c}$$
Still work when complex numbers are in the exponent ? For example, do these egalities are true ?
$$2^{4+2i}+2^{3+4i} = 2^{7+6i}$$ $$(2^{4+2i})^{3+4i}=4^{(4+2i)\:\cdot \:(3+4i)}$$
in that case using $\omega$ seems useful which implies $e^{\frac{2\pi i}{k}}$ for specific $k \in \mathbb {R^+}$ and $i$ is of course imaginary numbers
and as this implies angular coordinates on complex numbers then over I think