Complex Numbers and Exponents: Is z^0 Always Equal to 1?

[Hepic]

Lets say z!=0, and zeC(is complex).
So for example is z=2+3i.
z^0=1 => (2+3i)^0=1. I am correct? I know that all numbers in zero make us one,but it works with complex numbers too?

 

[arildno]

Yes.
It works in the case of complex numbers as well.

In general, though, the topic of exponentiation and logarithms of complex numbers is a nasty subject, where we have to be very careful when dealing with them.

 

[Hepic]

Alright. Thank you !