nthRoot method

List<Complex> nthRoot(int n)

ComplexRootsX

Computes the n-th roots of this complex number.

The nth roots are defined by the formula:

z_k = abs^(1/n) (cos(phi + 2πk/n) + i (sin(phi + 2πk/n))

for k=0, 1, ..., n-1, where abs and phi are respectively the modulus and argument of this complex number.

If one or both parts of this complex number is NaN, a list with just one element, nan is returned. If neither part is NaN, but at least one part is infinite, the result is a one-element list containing infinity.

Implementation

List<Complex> nthRoot(int n) {
  if (n <= 0) {
    throw ArgumentError("Can't compute nth root for negative n");
  }

  if (isNaN) {
    return [Complex.nan];
  } else if (isInfinite) {
    return [Complex.infinity];
  }

  // nth root of abs -- faster / more accurate to use a solver here?
  final nthRootOfAbs = math.pow(abs(), 1.0 / n).toDouble();

  // Compute nth roots of complex number with k = 0, 1, ... n-1
  final nthPhi = argument() / n;
  final slice = 2 * math.pi / n;
  var innerPart = nthPhi;
  return List.generate(n, (_) {
    final c = Complex.polar(nthRootOfAbs, innerPart);
    innerPart += slice;
    return c;
  });
}