If z=12+5i , then verify that
(1) (z bar) =z
(2) z+zbar =2 Re (z)
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2) lhs = 12+5i+(12+5ibar)
if the bar we have so imaginary Will minus
=12+5i+12-5i
+5i -5i will get cancel
the lhs is 12+12=24=2(12)
rhs =2 re(z)
the real number of z is 12
=2(12)
hence lhs=rhs
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