My implementation of the Newtonian Cube Root Approximation using complex numbers in Go. Part of the Go tour: http://tour.golang.org/#47

NewtonianCubeRoot.go

package main

import "fmt"
import "math/cmplx"
import "math"

const(
    ACCURACY_DELTA = 0.0000000000000001
)

func Cbrt(x complex128) complex128 {
    
	ourGuess := complex128(1) // any initial guess will do!
    
    for newtonGuess := newtonIteration(x, ourGuess); cmplx.Abs(newtonGuess-ourGuess) > ACCURACY_DELTA
    {
    	ourGuess = newtonGuess;
        newtonGuess = newtonIteration(x, ourGuess)
    }
        
    return ourGuess
}
 
func newtonIteration(x, z complex128) complex128{
    return z-(cmplx.Pow(z,3)-x)/cmplx.Pow(3*z,2)
}

func main() {
    fmt.Println("Newtonian Complex Cube Root:", Cbrt(2))
    fmt.Println("Non-Complex Control:", math.Cbrt(2))
}