I recall reading somewhere that is calculable (I think its a real number), so I was pondering whether or not this was true for complex numbers in general?
I recall reading somewhere that is calculable (I think its a real number), so I was pondering whether or not this was true for complex numbers in general?
There's no such thing as , you can only take a natural logarithm of positive real numbers.
However, is acceptable. It is also needed to be able to write the answer explicitly in terms of its real and imaginary parts.
Rubbish, you just did or rather discovered its extension (note it is multi-valued, and we will need that if we are going to use it to take powers of complex numbers).