nthRoots method

List<Complex> nthRoots(int n)

Calculate all nth roots of the complex number.

Throw ArgumentError if n is not positive.

Implementation

List<Complex> nthRoots(int n) {
  if (n <= 0) {
    throw ArgumentError('n must be a positive integer.');
  }
  final roots = <Complex>[];
  //    1. Calculates the nth root of the modulus r.
  //    Maintains maximum double precision.
  final double rRoot = math.pow(modulus, 1 / n).toDouble();

  for (int k = 0; k < n; k++) {
    // 2. Calculate the angle of the k-th root.
    //    Maintains maximum double precision.
    final angle = ((theta1 + (2 * math.pi * k)) / n);

    // 3. Calculate the real and imaginary parts.
    final real = rRoot * math.cos(angle);
    final imag = rRoot * math.sin(angle);

    //   4. Create the Complex object (using _service for efficiency).
    //   Note: ‘angle’ is the same for both theta1 and theta2 in this context.

    roots.add(Complex._service(real, imag, rRoot, angle, angle));
  }
  return roots;
}