@rayyamhk/complex/lib/core/instance/getArgument.js

A lightweight and easy-to-use library for you to manipulate complex numbers

"use strict";

/**
 * Calculates the argument of a Complex Number which is restricted to the interval [ 0, 2π ).<br><br>
 * 
 * The argument of the Complex Number is the angle between positive real-axis
 * and the vector representing the Complex Number on Complex plane.<br><br>
 * 
 * If the given Complex Number is considered as 0, returns undefined.
 * @memberof Complex
 * @instance
 * @returns {number} The argument of the Complex Number
 */
function getArgument() {
  var x = this.re;
  var y = this.im;
  var epsilon = 1 / (Math.pow(10, 15) * 2);

  if (Math.abs(x) < epsilon && Math.abs(y) < epsilon) {
    return undefined;
  }

  if (x === 0) {
    if (y > 0) {
      return Math.PI * 0.5;
    }

    return Math.PI * 1.5;
  }

  if (y === 0) {
    if (x > 0) {
      return 0;
    }

    return Math.PI;
  }

  if (x > 0 && y > 0) {
    return Math.atan(y / x);
  }

  if (x < 0 && y > 0) {
    return Math.PI - Math.atan(y / (x * -1));
  }

  if (x < 0 && y < 0) {
    return Math.PI + Math.atan(y * -1 / (x * -1));
  }

  return Math.PI * 2 - Math.atan(y * -1 / x);
}

module.exports = getArgument;