How do you find the principal value of 1^(3i)?
As well, (1-i*sqrt(3))^(1+pi*i)
Thanks
For $\displaystyle z\not = 0$ write $\displaystyle z=re^{i\theta}, \theta \in (-\pi,\pi]$.
Define, $\displaystyle \log z = \ln (r) + i \theta$.
Define, $\displaystyle a^b = e^{b\log a}, a\not = 0$ for $\displaystyle a,b\in \mathbb{C}$.
Can you solve your problem now?