package main

import (
	"fmt"
	"math/cmplx"
)

const threshold = 1e-5

func Cbrt(x complex128) (z complex128) {
	z = x
	for delta, last := 1e9, z; delta > threshold; last = z {
		z -= (z*z*z - x) / (3 * z * z)
		delta = cmplx.Abs(z - last)
	}
	return
}

func main() {
	n := 12392.13 + 1982i
	fmt.Println("calculated ", Cbrt(n))
	fmt.Println("expected   ", cmplx.Pow(n, 1/3.0))
}