Complex.js

module.exports = Complex;
function Complex(real, imag) {

  this.getReal = function () {
    return real;
  };

  this.getImaginary = function () {
    return imag;
  }

  this.getModulus = function () {
    return Math.sqrt(real*real + imag*imag);
  };

  this.getConjugate = function () {
    return new Complex(real, -imag);
  };

  this.getArgument = function () {
    return Math.atan2(imag, real);
  };

  this.add      = function (num) { return Complex.add(this, num); };
  this.subtract = function (num) { return Complex.subtract(this, num); };
  this.multiply = function (num) { return Complex.multiply(this, num); };
  this.divide   = function (num) { return Complex.divide(this, num); }

  this.divide = function (num) {
    return Complex.divide(this, num);
  }

  this.toString = function () {
    if (real === 0 && imag !== 0) {
      return imag + 'i';
    } else if (imag === 0 && real !== 0) {
      return real.toString();
    } else if (imag === 0 && real === 0) {
      return 0;
    }

    return real.toString() + (imag < 0 ? ' - ' + imag : ' + ' + imag) + 'i';
  };
}

Complex.add = function (a, b) {
  return new Complex(a.getReal() + b.getReal(), a.getImaginary() + b.getImaginary());
}

Complex.subtract = function (a, b) {
  return new Complex(a.getReal() - b.getReal(), a.getImaginary() - b.getImaginary());
};

Complex.multiply = function (a, b) {
  return new Complex(
    a.getReal()*b.getReal() - a.getImaginary()*b.getImaginary(),
    a.getReal()*b.getImaginary() + b.getReal()*a.getImaginary()
  )
};

Complex.divide = function (a, b) {
  var dividend = a.multiply(b.getConjugate())
  var divisor  = b.getReal()*b.getReal() + b.getImaginary()*b.getImaginary();

  return new Complex(dividend.getReal() / divisor, dividend.getImaginary() / divisor);
};