/**
 * @license Complex.js v2.0.1 11/02/2016
 *
 * Copyright (c) 2016, Robert Eisele (robert@xarg.org)
 * Dual licensed under the MIT or GPL Version 2 licenses.
 **/

/**
 *
 * This class allows the manipilation of complex numbers.
 * You can pass a complex number in different formats. Either as object, double, string or two integer parameters.
 *
 * Object form
 * { re: <real>, im: <imaginary> }
 * { arg: <angle>, abs: <radius> }
 * { phi: <angle>, r: <radius> }
 *
 * Double form
 * 99.3 - Single double value
 *
 * String form
 * "23.1337" - Simple real number
 * "15+3i" - a simple complex number
 * "3-i" - a simple complex number
 *
 * Example:
 *
 * var c = new Complex("99.3+8i");
 * c.mul({r: 3, i: 9}).div(4.9).sub(3, 2);
 *
 */

(function(root) {

  "use strict";

  var P = {'re': 0, 'im': 0};

  Math.cosh = Math.cosh || function(x) {
    return (Math.exp(x) + Math.exp(-x)) * 0.5;
  };

  Math.sinh = Math.sinh || function(x) {
    return (Math.exp(x) - Math.exp(-x)) * 0.5;
  };

  var parser_exit = function() {
    throw SyntaxError("Invalid Param");
  };

  /**
   * Calculates log(sqrt(a^2+b^2)) in a way to avoid overflows
   *
   * @param {number} a
   * @param {number} b
   * @returns {number}
   */
  function logHypot(a, b) {

    var _a = Math.abs(a);
    var _b = Math.abs(b);

    if (a === 0) {
      return Math.log(_b);
    }

    if (b === 0) {
      return Math.log(_a);
    }

    if (_a < 3000 && _b < 3000) {
      return Math.log(a * a + b * b) * 0.5;
    }

    /* I got 4 ideas to compute this property without overflow:
     *
     * Testing 1000000 times with random samples for a,b ∈ [1, 1000000000] against a big decimal library to get an error estimate
     *
     * 1. Only eliminate the square root: (OVERALL ERROR: 3.9122483030951116e-11)

     Math.log(a * a + b * b) / 2

     *
     *
     * 2. Try to use the non-overflowing pythagoras: (OVERALL ERROR: 8.889760039210159e-10)

     var fn = function(a, b) {
     a = Math.abs(a);
     b = Math.abs(b);
     var t = Math.min(a, b);
     a = Math.max(a, b);
     t = t / a;

     return Math.log(a) + Math.log(1 + t * t) / 2;
     };

     * 3. Abuse the identity cos(atan(y/x) = x / sqrt(x^2+y^2): (OVERALL ERROR: 3.4780178737037204e-10)

     Math.log(a / Math.cos(Math.atan2(b, a)))

     * 4. Use 3. and apply log rules: (OVERALL ERROR: 1.2014087502620896e-9)

     Math.log(a) - Math.log(Math.cos(Math.atan2(b, a)))

     */

    return Math.log(a / Math.cos(Math.atan2(b, a)));
  }

  var parse = function(a, b) {

    if (a === undefined || a === null) {
      P["re"] =
      P["im"] = 0;
    } else if (b !== undefined) {
      P["re"] = a;
      P["im"] = b;
    } else switch (typeof a) {

      case "object":

        if ("im" in a && "re" in a) {
          P["re"] = a["re"];
          P["im"] = a["im"];
        } else if ("abs" in a && "arg" in a) {
          P["re"] = a["abs"] * Math.cos(a["arg"]);
          P["im"] = a["abs"] * Math.sin(a["arg"]);
        } else if ("r" in a && "phi" in a) {
          P["re"] = a["r"] * Math.cos(a["phi"]);
          P["im"] = a["r"] * Math.sin(a["phi"]);
        } else {
          parser_exit();
        }
        break;

      case "string":

        P["im"] = /* void */
        P["re"] = 0;

        var tokens = a.match(/\d+\.?\d*e[+-]?\d+|\d+\.?\d*|\.\d+|./g);
        var plus = 1;
        var minus = 0;

        if (tokens === null) {
          parser_exit();
        }

        for (var i = 0; i < tokens.length; i++) {

          var c = tokens[i];

          if (c === ' ' || c === '\t' || c === '\n') {
            /* void */
          } else if (c === '+') {
            plus++;
          } else if (c === '-') {
            minus++;
          } else if (c === 'i' || c === 'I') {

            if (plus + minus === 0) {
              parser_exit();
            }

            if (tokens[i + 1] !== ' ' && !isNaN(tokens[i + 1])) {
              P["im"]+= parseFloat((minus % 2 ? "-" : "") + tokens[i + 1]);
              i++;
            } else {
              P["im"]+= parseFloat((minus % 2 ? "-" : "") + "1");
            }
            plus = minus = 0;

          } else {

            if (plus + minus === 0 || isNaN(c)) {
              parser_exit();
            }

            if (tokens[i + 1] === 'i' || tokens[i + 1] === 'I') {
              P["im"]+= parseFloat((minus % 2 ? "-" : "") + c);
              i++;
            } else {
              P["re"]+= parseFloat((minus % 2 ? "-" : "") + c);
            }
            plus = minus = 0;
          }
        }

        // Still something on the stack
        if (plus + minus > 0) {
          parser_exit();
        }
        break;

      case "number":
        P["im"] = 0;
        P["re"] = a;
        break;

      default:
        parser_exit();
    }

    if (isNaN(P["re"]) || isNaN(P["im"])) {
      // If a calculation is NaN, we treat it as NaN and don't throw
      //parser_exit();
    }
  };

  /**
   * @constructor
   * @returns {Complex}
   */
  function Complex(a, b) {

    if (!(this instanceof Complex)) {
      return new Complex(a, b);
    }

    parse(a, b); // mutates P

    this["re"] = P["re"];
    this["im"] = P["im"];
  }

  Complex.prototype = {

    "re": 0,
    "im": 0,

    /**
     * Calculates the sign of a complex number
     *
     * @returns {Complex}
     */
    "sign": function() {

      var abs = this["abs"]();

      return new Complex(
              this["re"] / abs,
              this["im"] / abs);
    },

    /**
     * Adds two complex numbers
     *
     * @returns {Complex}
     */
    "add": function(a, b) {

      parse(a, b); // mutates P

      return new Complex(
              this["re"] + P["re"],
              this["im"] + P["im"]);
    },

    /**
     * Subtracts two complex numbers
     *
     * @returns {Complex}
     */
    "sub": function(a, b) {

      parse(a, b); // mutates P

      return new Complex(
              this["re"] - P["re"],
              this["im"] - P["im"]);
    },

    /**
     * Multiplies two complex numbers
     *
     * @returns {Complex}
     */
    "mul": function(a, b) {

      parse(a, b); // mutates P

      // Besides the addition/subtraction, this helps having a solution for rational Infinity
      if (P['im'] === 0 && this['im'] === 0) {
        return new Complex(this['re'] * P['re'], 0);
      }

      return new Complex(
              this["re"] * P["re"] - this["im"] * P["im"],
              this["re"] * P["im"] + this["im"] * P["re"]);
    },

    /**
     * Divides two complex numbers
     *
     * @returns {Complex}
     */
    "div": function(a, b) {

      parse(a, b); // mutates P

      a = this["re"];
      b = this["im"];

      var c = P["re"];
      var d = P["im"];
      var t, x;

      // Divisor is zero
      if (0 === c && 0 === d) {
        return new Complex(
                (a !== 0) ? (a / 0) : 0,
                (b !== 0) ? (b / 0) : 0);
      }

      // Divisor is rational
      if (0 === d) {
        return new Complex(a / c, b / c);
      }

      if (Math.abs(c) < Math.abs(d)) {

        x = c / d;
        t = c * x + d;

        return new Complex(
                (a * x + b) / t,
                (b * x - a) / t);

      } else {

        x = d / c;
        t = d * x + c;

        return new Complex(
                (a + b * x) / t,
                (b - a * x) / t);
      }
    },

    /**
     * Calculate the power of two complex numbers
     *
     * @returns {Complex}
     */
    "pow": function(a, b) {

      parse(a, b); // mutates P

      a = this["re"];
      b = this["im"];

      if (a === 0 && b === 0) {
        return new Complex(0, 0);
      }

      var arg = Math.atan2(b, a);
      var loh = logHypot(a, b);

      if (P["im"] === 0) {

        if (b === 0 && a >= 0) {

          return new Complex(Math.pow(a, P["re"]), 0);

        } else if (a === 0) {

          switch (P["re"] % 4) {
            case 0:
              return new Complex(Math.pow(b, P["re"]), 0);
            case 1:
              return new Complex(0, Math.pow(b, P["re"]));
            case 2:
              return new Complex(-Math.pow(b, P["re"]), 0);
            case 3:
              return new Complex(0, -Math.pow(b, P["re"]));
          }
        }
      }

      /* I couldn"t find a good formula, so here is a derivation and optimization
       *
       * z_1^z_2 = (a + bi)^(c + di)
       *         = exp((c + di) * log(a + bi)
       *         = pow(a^2 + b^2, (c + di) / 2) * exp(i(c + di)atan2(b, a))
       * =>...
       * Re = (pow(a^2 + b^2, c / 2) * exp(-d * atan2(b, a))) * cos(d * log(a^2 + b^2) / 2 + c * atan2(b, a))
       * Im = (pow(a^2 + b^2, c / 2) * exp(-d * atan2(b, a))) * sin(d * log(a^2 + b^2) / 2 + c * atan2(b, a))
       *
       * =>...
       * Re = exp(c * log(sqrt(a^2 + b^2)) - d * atan2(b, a)) * cos(d * log(sqrt(a^2 + b^2)) + c * atan2(b, a))
       * Im = exp(c * log(sqrt(a^2 + b^2)) - d * atan2(b, a)) * sin(d * log(sqrt(a^2 + b^2)) + c * atan2(b, a))
       *
       * =>
       * Re = exp(c * logsq2 - d * arg(z_1)) * cos(d * logsq2 + c * arg(z_1))
       * Im = exp(c * logsq2 - d * arg(z_1)) * sin(d * logsq2 + c * arg(z_1))
       *
       */

      a = Math.exp(P["re"] * loh - P["im"] * arg);
      b = P["im"] * loh + P["re"] * arg;
      return new Complex(
              a * Math.cos(b),
              a * Math.sin(b));
    },

    /**
     * Calculate the complex square root
     *
     * @returns {Complex}
     */
    "sqrt": function() {

      var a = this["re"];
      var b = this["im"];
      var r = this["abs"]();

      var re, im;

      if (a >= 0 && b === 0) {
        return new Complex(Math.sqrt(a), 0);
      }

      if (a >= 0) {
        re = 0.5 * Math.sqrt(2.0 * (r + a));
      } else {
        re = Math.abs(b) / Math.sqrt(2 * (r - a));
      }

      if (a <= 0) {
        im = 0.5 * Math.sqrt(2.0 * (r - a));
      } else {
        im = Math.abs(b) / Math.sqrt(2 * (r + a));
      }

      return new Complex(re, b >= 0 ? im : -im);
    },

    /**
     * Calculate the complex exponent
     *
     * @returns {Complex}
     */
    "exp": function() {

      var tmp = Math.exp(this["re"]);

      if (this["im"] === 0) {
        //return new Complex(tmp, 0);
      }
      return new Complex(
              tmp * Math.cos(this["im"]),
              tmp * Math.sin(this["im"]));
    },

    /**
     * Calculate the natural log
     *
     * @returns {Complex}
     */
    "log": function() {

      var a = this["re"];
      var b = this["im"];
      
      if (b === 0 && a > 0) {
        //return new Complex(Math.log(a), 0);
      }

      return new Complex(
              logHypot(a, b),
              Math.atan2(b, a));
    },

    /**
     * Calculate the magniture of the complex number
     *
     * @returns {number}
     */
    "abs": function() {

      var a = Math.abs(this["re"]);
      var b = Math.abs(this["im"]);

      if (a < 3000 && b < 3000) {
        return Math.sqrt(a * a + b * b);
      }

      if (a < b) {
        a = b;
        b = this["re"] / this["im"];
      } else {
        b = this["im"] / this["re"];
      }
      return a * Math.sqrt(1 + b * b);
    },

    /**
     * Calculate the angle of the complex number
     *
     * @returns {number}
     */
    "arg": function() {

      return Math.atan2(this["im"], this["re"]);
    },

    /**
     * Calculate the sine of the complex number
     *
     * @returns {Complex}
     */
    "sin": function() {

      var a = this["re"];
      var b = this["im"];

      return new Complex(
              Math.sin(a) * Math.cosh(b),
              Math.cos(a) * Math.sinh(b));
    },

    /**
     * Calculate the cosine
     *
     * @returns {Complex}
     */
    "cos": function() {

      var a = this["re"];
      var b = this["im"];

      return new Complex(
              Math.cos(a) * Math.cosh(b),
             -Math.sin(a) * Math.sinh(b));
    },

    /**
     * Calculate the tangent
     *
     * @returns {Complex}
     */
    "tan": function() {

      var a = 2 * this["re"];
      var b = 2 * this["im"];
      var d = Math.cos(a) + Math.cosh(b);

      return new Complex(
              Math.sin(a) / d,
              Math.sinh(b) / d);
    },

    /**
     * Calculate the cotangent
     *
     * @returns {Complex}
     */
    "cot": function() {

      var a = 2 * this["re"];
      var b = 2 * this["im"];
      var d = Math.cos(a) - Math.cosh(b);

      return new Complex(
             -Math.sin(a) / d,
              Math.sinh(b) / d);
    },

    /**
     * Calculate the secant
     *
     * @returns {Complex}
     */
    "sec": function() {

      var a = this["re"];
      var b = this["im"];
      var d = 0.5 * Math.cosh(2 * b) + 0.5 * Math.cos(2 * a);

      return new Complex(
              Math.cos(a) * Math.cosh(b) / d,
              Math.sin(a) * Math.sinh(b) / d);
    },

    /**
     * Calculate the cosecans
     *
     * @returns {Complex}
     */
    "csc": function() {

      var a = this["re"];
      var b = this["im"];
      var d = 0.5 * Math.cosh(2 * b) - 0.5 * Math.cos(2 * a);

      return new Complex(
              Math.sin(a) * Math.cosh(b) / d,
             -Math.cos(a) * Math.sinh(b) / d);
    },

    /**
     * Calculate the complex arcus sinus
     *
     * @returns {Complex}
     */
    "asin": function() {

      var a = this["re"];
      var b = this["im"];

      var t1 = new Complex(
               b * b - a * a + 1,
              -2 * a * b)['sqrt']();

      var t2 = new Complex(
              t1['re'] - b,
              t1['im'] + a)['log']();

      return new Complex(t2['im'], -t2['re']);
    },

    /**
     * Calculate the complex arcus cosinus
     *
     * @returns {Complex}
     */
    "acos": function() {

      var a = this["re"];
      var b = this["im"];

      var t1 = new Complex(
               b * b - a * a + 1,
              -2 * a * b)['sqrt']();

      var t2 = new Complex(
              t1["re"] - b,
              t1["im"] + a)['log']();

      return new Complex(Math.PI / 2 - t2["im"], t2["re"]);
    },

    /**
     * Calculate the complex arcus tangent
     *
     * @returns {Complex}
     */
    "atan": function() {

      var a = this["re"];
      var b = this["im"];

      if (a === 0) {

        if (b === 1) {
          return new Complex(0, Infinity);
        }

        if (b === -1) {
          return new Complex(0, -Infinity);
        }
      }

      var d = a * a + (1.0 - b) * (1.0 - b);

      var t1 = new Complex(
              (1 - b * b - a * a) / d,
              -2 * a / d).log();

      return new Complex(-0.5 * t1["im"], 0.5 * t1["re"]);
    },

    /**
     * Calculate the complex arcus cotangent
     *
     * @returns {Complex}
     */
    "acot": function() {

      var a = this["re"];
      var b = this["im"];

      if (b === 0) {
        return new Complex(Math.atan2(1, a), 0);
      }

      var d = a * a + b * b;
      return (d !== 0)
              ? new Complex(
                      a / d,
                     -b / d).atan()
              : new Complex(
                      (a !== 0) ? a / 0 : 0,
                      (b !== 0) ?-b / 0 : 0).atan();
    },

    /**
     * Calculate the complex arcus secant
     *
     * @returns {Complex}
     */
    "asec": function() {

      var a = this["re"];
      var b = this["im"];

      if (a === 0 && b === 0) {
        return new Complex(0, Infinity);
      }

      var d = a * a + b * b;
      return (d !== 0)
              ? new Complex(
                      a / d,
                      -b / d).acos()
              : new Complex(
                      (a !== 0) ? a / 0 : 0,
                      (b !== 0) ?-b / 0 : 0).acos();
    },

    /**
     * Calculate the complex arcus cosecans
     *
     * @returns {Complex}
     */
    "acsc": function() {

      var a = this["re"];
      var b = this["im"];

      if (a === 0 && b === 0) {
        return new Complex(Math.PI / 2, Infinity);
      }

      var d = a * a + b * b;
      return (d !== 0)
              ? new Complex(
                      a / d,
                     -b / d).asin()
              : new Complex(
                      (a !== 0) ? a / 0 : 0,
                      (b !== 0) ?-b / 0 : 0).asin();
    },

    /**
     * Calculate the complex sinh
     *
     * @returns {Complex}
     */
    "sinh": function() {

      var a = this["re"];
      var b = this["im"];

      return new Complex(
              Math.sinh(a) * Math.cos(b),
              Math.cosh(a) * Math.sin(b));
    },

    /**
     * Calculate the complex cosh
     *
     * @returns {Complex}
     */
    "cosh": function() {

      var a = this["re"];
      var b = this["im"];

      return new Complex(
              Math.cosh(a) * Math.cos(b),
              Math.sinh(a) * Math.sin(b));
    },

    /**
     * Calculate the complex tanh
     *
     * @returns {Complex}
     */
    "tanh": function() {

      var a = 2 * this["re"];
      var b = 2 * this["im"];
      var d = Math.cosh(a) + Math.cos(b);

      return new Complex(
              Math.sinh(a) / d,
              Math.sin(b) / d);
    },

    /**
     * Calculate the complex coth
     *
     * @returns {Complex}
     */
    "coth": function() {

      var a = 2 * this["re"];
      var b = 2 * this["im"];
      var d = Math.cosh(a) - Math.cos(b);

      return new Complex(
              Math.sinh(a) / d,
             -Math.sin(b) / d);
    },

    /**
     * Calculate the complex coth
     *
     * @returns {Complex}
     */
    "csch": function() {

      var a = this["re"];
      var b = this["im"];
      var d = Math.cos(2 * b) - Math.cosh(2 * a);

      return new Complex(
           -2 * Math.sinh(a) * Math.cos(b) / d, 
            2 * Math.cosh(a) * Math.sin(b) / d);
    },

    /**
     * Calculate the complex sech
     *
     * @returns {Complex}
     */
    "sech": function() {

      var a = this["re"];
      var b = this["im"];
      var d = Math.cos(2 * b) + Math.cosh(2 * a);

      return new Complex(
              2 * Math.cosh(a) * Math.cos(b) / d, 
             -2 * Math.sinh(a) * Math.sin(b) / d);
    },

    /**
     * Calculate the complex asinh
     *
     * @returns {Complex}
     */
    "asinh": function() {

      var tmp = this["im"];
      this["im"] = -this["re"];
      this["re"] = tmp;
      var res = this["asin"]();

      this["re"] = -this["im"];
      this["im"] = tmp;
      tmp = res["re"];

      res["re"] = -res["im"];
      res["im"] = tmp;
      return res;
    },

    /**
     * Calculate the complex asinh
     *
     * @returns {Complex}
     */
    "acosh": function() {

      var tmp;
      var res = this["acos"]();
      if (res["im"] <= 0) {
        tmp = res["re"];
        res["re"] = -res["im"];
        res["im"] = tmp;
      } else {
        tmp = res["im"];
        res["im"] = -res["re"];
        res["re"] = tmp;
      }
      return res;
    },

    /**
     * Calculate the complex atanh
     *
     * @returns {Complex}
     */
    "atanh": function() {

      var a = this["re"];
      var b = this["im"];

      var noIM = a > 1 && b === 0;
      var oneMinus = 1 - a;
      var onePlus = 1 + a;
      var d = oneMinus * oneMinus + b * b;

      var x = (d !== 0)
              ? new Complex(
                      (onePlus * oneMinus - b * b) / d,
                      (b * oneMinus + onePlus * b) / d)
              : new Complex(
                      (a !== -1) ? (a / 0) : 0,
                      (b !== 0) ? (b / 0) : 0);

      var temp = x["re"];
      x["re"] = logHypot(x["re"], x["im"]) / 2;
      x["im"] = Math.atan2(x["im"], temp) / 2;
      if (noIM) {
        x["im"] = -x["im"];
      }
      return x;
    },

    /**
     * Calculate the complex acoth
     *
     * @returns {Complex}
     */
    "acoth": function() {

      var a = this["re"];
      var b = this["im"];

      if (a === 0 && b === 0) {

        return new Complex(0, Math.PI / 2);
      }

      var d = a * a + b * b;
      return (d !== 0)
              ? new Complex(
                      a / d,
                     -b / d).atanh()
              : new Complex(
                      (a !== 0) ? a / 0 : 0,
                      (b !== 0) ?-b / 0 : 0).atanh();
    },

    /**
     * Calculate the complex acsch
     *
     * @returns {Complex}
     */
    "acsch": function() {

      var a = this["re"];
      var b = this["im"];

      if (b === 0) {

        return new Complex(
                (a !== 0)
                ? Math.log(a + Math.sqrt(a * a + 1))
                : Infinity, 0);
      }

      var d = a * a + b * b;
      return (d !== 0)
              ? new Complex(
                      a / d,
                      -b / d).asinh()
              : new Complex(
                      (a !== 0) ? a / 0 : 0,
                      (b !== 0) ?-b / 0 : 0).asinh();
    },

    /**
     * Calculate the complex asech
     *
     * @returns {Complex}
     */
    "asech": function() {

      var a = this["re"];
      var b = this["im"];

      if (a === 0 && b === 0) {
        return new Complex(Infinity, 0);
      }

      var d = a * a + b * b;
      return (d !== 0)
              ? new Complex(
                      a / d,
                     -b / d).acosh()
              : new Complex(
                      (a !== 0) ? a / 0 : 0,
                      (b !== 0) ?-b / 0 : 0).acosh();
    },

    /**
     * Calculate the complex inverse 1/z
     *
     * @returns {Complex}
     */
    "inverse": function() {

      var a = this["re"];
      var b = this["im"];

      var d = a * a + b * b;

      return new Complex(
              a !== 0 ? a / d : 0,
              b !== 0 ?-b / d : 0);
    },

    /**
     * Returns the complex conjugate
     *
     * @returns {Complex}
     */
    "conjugate": function() {

      return new Complex(this["re"], -this["im"]);
    },

    /**
     * Gets the negated complex number
     *
     * @returns {Complex}
     */
    "neg": function() {

      return new Complex(-this["re"], -this["im"]);
    },

    /**
     * Ceils the actual complex number
     *
     * @returns {Complex}
     */
    "ceil": function(places) {

      places = Math.pow(10, places || 0);

      return new Complex(
              Math.ceil(this["re"] * places) / places,
              Math.ceil(this["im"] * places) / places);
    },

    /**
     * Floors the actual complex number
     *
     * @returns {Complex}
     */
    "floor": function(places) {

      places = Math.pow(10, places || 0);

      return new Complex(
              Math.floor(this["re"] * places) / places,
              Math.floor(this["im"] * places) / places);
    },

    /**
     * Ceils the actual complex number
     *
     * @returns {Complex}
     */
    "round": function(places) {

      places = Math.pow(10, places || 0);

      return new Complex(
              Math.round(this["re"] * places) / places,
              Math.round(this["im"] * places) / places);
    },

    /**
     * Compares two complex numbers
     *
     * @returns {boolean}
     */
    "equals": function(a, b) {

      parse(a, b); // mutates P

      return Math.abs(P["re"] - this["re"]) <= Complex["EPSILON"] &&
             Math.abs(P["im"] - this["im"]) <= Complex["EPSILON"];
    },

    /**
     * Clones the actual object
     *
     * @returns {Complex}
     */
    "clone": function() {

      return new Complex(this["re"], this["im"]);
    },

    /**
     * Gets a string of the actual complex number
     *
     * @returns {string}
     */
    "toString": function() {

      var a = this["re"];
      var b = this["im"];
      var ret = "";

      if (isNaN(a) || isNaN(b)) {
        return "NaN";
      }

      if (a !== 0) {
        ret+= a;
      }

      if (b !== 0) {

        if (a !== 0) {
          ret+= b < 0 ? " - " : " + ";
        } else if (b < 0) {
          ret+= "-";
        }

        b = Math.abs(b);

        if (1 !== b) {
          ret+= b;
        }
        ret+= "i";
      }

      if (!ret)
        return "0";

      return ret;
    },

    /**
     * Returns the actual number as a vector
     *
     * @returns {Array}
     */
    "toVector": function() {

      return [this["re"], this["im"]];
    },

    /**
     * Returns the actual real value of the current object
     *
     * @returns {number|null}
     */
    "valueOf": function() {

      if (this["im"] === 0) {
        return this["re"];
      }
      return null;
    },

    /**
     * Checks if the given complex number is not a number
     *
     * @returns {boolean}
     */
    isNaN: function() {
      return isNaN(this['re']) || isNaN(this['im']);
    }
  };

  Complex["ZERO"] = new Complex(0, 0);
  Complex["ONE"] = new Complex(1, 0);
  Complex["I"] = new Complex(0, 1);
  Complex["PI"] = new Complex(Math.PI, 0);
  Complex["E"] = new Complex(Math.E, 0);
  Complex['EPSILON'] = 1e-16;

  if (typeof define === "function" && define["amd"]) {
    define([], function() {
      return Complex;
    });
  } else if (typeof exports === "object") {
    module["exports"] = Complex;
  } else {
    root["Complex"] = Complex;
  }
  
})(this);