Solve the equation `(x-1)^3+8=0` in the set C of all complex numbers.

Explanation

We have,
`(x-1)^(3) + 8 =0 pr (x-1)^(3) = -8 or x - 1 (-8)^(1//3)`
or ` x -1= 2(-1)^(1//3)`
or `x-1 = 2(-1) or x - 1 =2 (-omega) or x-1 = 2(-omega^(2)) " "[because (-1)^(1//3) = -1 or -omega or -omega^(2)]`
`x -1 = -2 or x - 1 = -2omega or x - 1 = - 2omega^(2)`
`or x = -1 or x =1 -2 omega or x = 1- 2omega^(2)`
Hence , the solution of the equations `(x-1)^(3) + 8 = 0` are `-1,1,-2omega` and `1-2omega^(2)`.