/*
basic complex number arithmetic from
http://rosettacode.org/wiki/Fast_Fourier_transform#Scala
*/
function Complex(re, im)
{
	this.re = re;
	this.im = im || 0.0;
}
Complex.prototype.add = function(other, dst)
{
	dst.re = this.re + other.re;
	dst.im = this.im + other.im;
	return dst;
}
Complex.prototype.sub = function(other, dst)
{
	dst.re = this.re - other.re;
	dst.im = this.im - other.im;
	return dst;
}
Complex.prototype.mul = function(other, dst)
{
	//cache re in case dst === this
	var r = this.re * other.re - this.im * other.im;
	dst.im = this.re * other.im + this.im * other.re;
	dst.re = r;
	return dst;
}
Complex.prototype.cexp = function(dst)
{
	var er = Math.exp(this.re);
	dst.re = er * Math.cos(this.im);
	dst.im = er * Math.sin(this.im);
	return dst;
}
Complex.prototype.log = function()
{
	/*
	although 'It's just a matter of separating out the real and imaginary parts of jw.' is not a helpful quote
	the actual formula I found here and the rest was just fiddling / testing and comparing with correct results.
	http://cboard.cprogramming.com/c-programming/89116-how-implement-complex-exponential-functions-c.html#post637921
	*/
	if( !this.re )
		console.log(this.im.toString()+'j');
	else if( this.im < 0 )
		console.log(this.re.toString()+this.im.toString()+'j');
	else
		console.log(this.re.toString()+'+'+this.im.toString()+'j');
}