Complex.js

/* 
 implement complex mathamatic property using JS Object
*/

//  Define constructor : ===================================================================
//  ( c = x + y i )
//  ========================================================================================
function Complex(real,imaginary){
  this.x = real;
  this.y = imaginary;
}

//  Define instance property:  =============================================================
//  (check "Complex.prototype" as well)
//  ========================================================================================

// the distance from (0,0) = x^2+y^2
Complex.prototype.magnitude = function(){
  return Math.sqrt(this.x*this.x + this.y*this.y);
}

// -c = - ( x + y i )
Complex.prototype.negative = function(){
  return new Complex(-this.x,-this.y);
}

// overwrite toString method
Complex.prototype.toString = function(){
  return "(" + this.x + "," + this.y + ")";
}

// real(x) as the basic value
Complex.prototype.valueOf = function(){ return this.x ;}

//  Define class property:  ===============================================================
//  (check "Complex.hasOwnProperty('{prperty name}')" as well)
//  ========================================================================================

// c1+c2 = ( x1+x2 , y1+y2 )
Complex.add = function(a,b){
 return new Complex( a.x + b.x , a.y + b.y );
}

// c1-c2 = ( x1-x2 , y1-y2 )
Complex.subtract = function(a,b){
  return new Complex( a.x - b.x , a.y - b.y );
}

// c1*c2 = ( x1*x2 , y1*y2 )
Complex.multiply = function(a,b){
  return new Complex( a.x * b.x , a.y * b.y );
}

// define 0,1,i as class property
Complex.zero = new Complex(0,0);
Complex.one = new Complex(1,0);
Complex.i = new Complex(0,1);

//  Evaluattion ( not neccesary)  ============================================================= 

console.log(Complex.prototype);
var c1 = new Complex(-1,3);
var c2 = new Complex(2,0.5);
c1.magnitude();
Complex.add(c1,c2);
Complex.subtract(c2,Complex.i);

// Plus =====================================================================================

c1.constructor == Complex;  //true
c1.constructor == Object;  //false
Complex.prototype.isPrototypeOf(c1); // true
Object.prototype.isPrototypeOf(c1);  // true
c1 instanceof Complex; // true
c1 instanceof Object; // true