Complex.ele

struct Complex(real:Num, imag:Num)
{
    zero = Complex(0, 0)
    unitReal = Complex(1, 0)
    unitImag = Complex(0, 1)

    #[[ Create a Complex number from its polar coordinates
    #   The angle must be in radians
    #]]
    fromPolar(r:Num, theta:Num):Complex
    {
        x = r.mul(Num.cos(theta))
        y = r.mul(Num.sin(theta))
        return = Complex(x, y)
    }

    conjugate(c:Complex):Complex = Complex(c.real, c.imag.mul(-1))

    modulusSquared(c:Complex):Num = c.mul(c.conjugate).real
    modulus(c:Complex):Num = Num.sqrt(c.modulusSquared)

    #[[ Get the polar angle of the number in radians
    #   Result is between -pi and pi
    #]]
    argument(c:Complex):Num
    {
        angle = Num.acos(c.real.div(c.modulus))
        angleSign = if(c.imag.geq(0), 1, -1)
        return = angle.mul(angleSign)
    }

    scale(c:Complex, n:Num) = Complex(c.real.mul(n), c.imag.mul(n))

    add(u:Complex, v:Complex):Complex = Complex(u.real.add(v.real), u.imag.add(v.imag))
    sub(u:Complex, v:Complex):Complex = Complex(u.real.sub(v.real), u.imag.sub(v.imag))

    mul(u:Complex, v:Complex):Complex
    {
        newReal = u.real.mul(v.real).sub(u.imag.mul(v.imag))
        newImaginary = u.real.mul(v.imag).add(u.imag.mul(v.real))
        return = Complex(newReal, newImaginary)
    }

    div(u:Complex, v:Complex):Complex
    {
        denominator = v.modulusSquared
        numerator = u.mul(v.conjugate)
        return = numerator.scale(1.div(denominator))
    }
}