We know that . Then let .
We see that so we have one fourth root.
If then the four roots are .
Thanks a lot!
I have one question though...I understand everything but the last line, where I get a bit confused. The result would be equivalent to (-1)^(1/4)*(-1)^(1/2)*k, but why the second bit? ((-1)^(1/2)*k)
Thanks for your help, and sorry for bothering you again :-/
You can also use this formula:
Where r is the modulus and theta the angle.
For your example, the modulus of is .
And the angle is since the coordinates are (-1,0).
N is the number of roots and k=0,1,2,3.
Therefore, you would solve
This is the Principle root of
and do the same for w_2 and w_3. Also, once you solve w_0, you can divide by 4 to figure out the other roots with out using the formula.