I want to find the 6th root of z which lies in a specific domain.

227 Views Asked by At

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} $

1

There are 1 best solutions below

4
On BEST ANSWER

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...