The question

Find the cartesian form of the principle value of:

$\displaystyle ((\frac{1 + i\sqrt{3}}{2})^{-3})^{1 - i}$

My attempt

$\displaystyle e^{(1 - i)Log(e^{(\frac{\pi i}{3})}^{-3})$

$\displaystyle e^{(1 - i)Log(e^{-\pi i}})$

$\displaystyle e^{(1 - i)(ln|1| + i(-\pi))}$ //uh oh, this is on a branch cut!

How do I proceed, if the principle Log is not defined on the negative real axis?

Thank you.