`x ^ n`

is the exponentiation operation, not the root finder. If you want to find all the roots of a complex number, you can for example search for the roots of the corresponding polynomial using `PolynomialRoots.jl`

(but there are also other packages for looking for roots of polynomials, like `Polynomials.jl`

):

```
julia> using PolynomialRoots
julia> roots([8, 0, 0, -1])
3-element Array{Complex{Float64},1}:
-1.0-1.73205im
2.0-9.61481e-17im
-1.0+1.73205im
```

The argument of `roots`

is the vector of coefficients of the polynomial, from the lowest to the highest one. This gives you the 3rd roots of 8.

In your case:

```
julia> roots([x, 0, 0, -1])
3-element Array{Complex{Float64},1}:
2.81908+1.02606im
-0.520945-2.95442im
-2.29813+1.92836im
```

Note also that for the exponentiation operation `x ^ (1/3)`

with `x`

real you can use instead `cbrt(x)`

, which is often faster and more accurate.