Tricky . . .
Find all roots of: .
We have: .
Since , we have: . . . . a sum of cubes
. . . . . . . . .
We have two equations to solve:
Quadratic Formula: .
The three roots are: .
I'm trying to work out the roots for the equation above. I've worked out one of them as being z = i, as z^3= i^3 = -i.
Wolfram Alpha gives
z = 1/2 (sqrt(3)-i) and z = 1/2 (-sqrt(3)-i)
as the other answers, but I'm unsure how they arrived at this?