Need help with complex numbers ..

Question

Hi!
Just want to check if i got it right - if anyone could pls confirm:
public void divComplex(Complex a, Complex b)
x = ((a.x * b.x) + (a.y * b.y))/((b.x * b.x) + (b.y * b.y));
y = ((a.y * b.x) + (a.x * b.x))/((b.x * b.x) + (b.y * b.y));
public void multComplex(Complex a, Complex b)
x = ((a.x * b.x) - (a.y * b.y));
y = ((a.x * b.y) + (a.y * b.x));
where:
protected double x;
protected double y;
is declared to represent the complex number .
Is this correct?
Siw

Answer 1

For the division you have,
a/b = a*b'/b*b' = a*b'/|b|
|b| = (b.x + ib.y)*(b.x - ib.y) = b.x*b.x + b.y*b.y
a*b' = (a.x + ia.y)*(b.x - ib.y) =
(a.x*b.x + a.y*b.y) + i(a.y*b.x - a.x*b.y)
There seems to be a slight mistake in the imaginary part (y).
y = a.y*b.x - a.x*b.y / (b.x*b.x + b.y*b.y);
But don't take my word for it. It's been ages since I did complex numbers -:)