I managed to get to the point where there is an infinite range of values (Problem & Ans Attached). I am confused how he put it in exp form.
I think you need to be more specific as to where you are at.
You should have
By deMoivre's theorem:
You do not have an infinite range, because you are given the conditions that
So you want to pick the values k for which the angle lies between and
These values of k are: (Note: it's 3, not -3 because your range includes , but not )
To put it into exponential form as required, you'll need euler's formula:
The other way is to remember that all the roots are evenly spaced around a circle. So if you can figure out the angle between them, you can keep adding this angle and find all the roots.
In your case, the real roots are easy ( )...
For the complex roots...
.
So all roots differ by an angle of . From here we can say the roots are:
.