Complex Number Division class - c++

Question

I'm trying to overload the operator to divide two complex numbers
Testing with 3+2i / 4 - 3i
complex g(3, 2);
complex f(4,-3);
cout << g / f << endl;
I added * -1.0 since we go
(4*4) + (3 * -3)i^2 in math which is 25
((3*4) + (3 * -3)* -1) is my intent
Testing I get -0.545455 - 1.72727i
While before I added the * 1.0 I got
0.24 +0.76i
Which is was very close to
0.24 + 0.68i
the answer
complex complex :: operator/ (complex& x) {
complex conjugate = x.conj();
double j = (real * conjugate.real) + (imag * conjugate.imag); // real
double u = (real * conjugate.imag) + (imag * conjugate.real); // imag
double h = (((conjugate.imag * imag)* -1.0) + (real * conjugate.real)) + ( (real*conjugate.imag) + (imag * conjugate.real));
return complex(j/h,u/h);
}

Answer 1

This is wrong:
double j = (real * conjugate.real) + (imag * conjugate.imag); // real
should be -, not +.
This is right:
double u = (real * conjugate.imag) + (imag * conjugate.real); // imag
Although both j and u are meaninglessly named.
What's going on here?
double h = (((conjugate.imag * imag)* -1.0) + (real * conjugate.real)) + ( (real*conjugate.imag) + (imag * conjugate.real));
The denominator is just x*conjugate which is:
double denom = x.real * x.real + x.imag * x.imag;
Side-note, you want to take your argument by reference to const.