# Math Help - Find the principal value

1. ## Find the principal value

How do you find the principal value of 1^(3i)?
As well, (1-i*sqrt(3))^(1+pi*i)

Thanks

2. Originally Posted by universalsandbox
How do you find the principal value of 1^(3i)?
As well, (1-i*sqrt(3))^(1+pi*i)

Thanks
For $z\not = 0$ write $z=re^{i\theta}, \theta \in (-\pi,\pi]$.
Define, $\log z = \ln (r) + i \theta$.

Define, $a^b = e^{b\log a}, a\not = 0$ for $a,b\in \mathbb{C}$.
Can you solve your problem now?