Suppose z and w are complez numbers. Prove the (z+wbar)(zbar+w) is real. P.S when it says bar next to the variable it means the line on top of it
If you let
\(z=a+bi\qquad and \qquad w=q+ri\) (where a,b,q and r are real)
then it is fairly easy to prove. Just do the substitution.
do the same for the other factor and then multiply them. The answer is real;
1) I am NOT "Melody"
2) I suppose you know what the "bar" means
3) Try writing z as a+bi, w as x+yi, and expanding.
4) Hmmm. I got this question on a test just yesterday, on an AoPS course. Not sure why you post it now. Is it possible that you are taking the test now???