Let $z=-3+8.5i$, $\arg z \in (-\pi,\pi]$.
Find the $6th$ root of $z$ which which lies in: $(2\pi\frac{4}{6},2\pi\frac{5}{6})$
Provide an answer to decimal places.
What is $\theta$ if the answer is in the form $\sqrt[6]{z}=r^{\frac1 6}e^{im}$ ?
where $m= \frac{\theta + 2\pi k}{6} $
The format of the answer gives you a very strong hint as to the method you should use.
You should express you complex number like that: $z=\alpha e^{i\phi}$
In that case $\alpha=\sqrt{3^2+8.5^2}$
and $\tan{\phi}=-\dfrac{8.5}{3}$
I think you can go from there...