nthRoot method

dynamic nthRoot(double nth, { bool allRoots = false, })

Get the nth root of the number

Implementation

dynamic nthRoot(double nth, {bool allRoots = false}) {
  Complex complex = Complex.zero();
  if (this is Integer ||
      this is Precision ||
      this is Double ||
      this is Real) {
    complex = Complex.fromReal(numberToNum(this));
  }
  if (this is Imaginary) {
    complex = Complex.num(Integer.zero, this as Imaginary);
  }
  if (this is Complex) {
    complex = this as Complex;
  }
  //Return all the complex numbers of the nth root
  if (allRoots) {
    var roots = <Complex>[];
    for (var k = 0; k < nth; k++) {
      var r = math.pow(abs().toDouble(), 1 / nth);
      var theta = (complex.phase.value + 2 * math.pi * k) / nth;
      roots.add(Complex(r * math.cos(theta), r * math.sin(theta)));
    }
    return roots;
  }

  // return the ony smallest positive complex number
  var isNegativeNth = nth < 0;
  var n = isNegativeNth ? -nth : nth;

  var a = 0.0;
  var b = 0.0;

  if (n == 0) {
    a = 1;
  } else {
    var length = math.pow(abs().toDouble(), 1.0 / n) as double;
    var angle =
        complex.phase < 0 ? complex.phase + (2 * math.pi) : complex.phase;
    angle /= n;
    a = length * math.cos(angle.toDouble());
    b = length * math.sin(angle.toDouble());
  }

  if (isNegativeNth) {
    final den = a * a + b * b;
    a /= den;
    b = -b / den;
  }

  return Complex(a, b);
}