[Bug middle-end/122082] complex multiply: w * conj(w) should have zero imaginary part

[tydeman at tybor dot com via Gcc-bugs]

https://gcc.gnu.org/bugzilla/show_bug.cgi?id=122082

--- Comment #3 from Fred J. Tydeman <tydeman at tybor dot com> ---
Complex multiply:

w * conj(w) 
== (x+I*y)*(x-I*y) 
== [x*x - (I*y)*(I*y)] + [I*x*y-I*x*y]
== [x*x - (I*I)*(y*y)] + [I*(x*y-*x*y)]
== [x*x - (-1)*(y*y)] + [I*(0)]
== [x*x + y*y] + I*0

So, the imaginary part of the product should be 0.