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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

Oct 29, 2020

#1
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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;

Oct 29, 2020
#2
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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???

Oct 29, 2020
#3
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hmm.. I don't know who you are

Oct 30, 2020