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

Guest Oct 29, 2020

#1**+1 **

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.

for example,

\((z+\bar w)=[a+bi+q-ri]=[(a+q)+(b-r)i]\)

do the same for the other factor and then multiply them. The answer is real;

Melody Oct 29, 2020