 #1
lema21
 18
 9
 Homework Statement:
 If z,w are in C then prove that bar(z/w) = bar(z)/bar(w).
 Relevant Equations:

z = a+bi
w = c+di
Bar(z) = abi
Bar(w) = cdi
I need help actually creating the proof. I've done the scratch needed for the problem, it's just forming the proof that I need help in.
Bar(a+bi/c+di)= (abi) / (cdi)
Bar ((a+bi/c+di)*(cdi/cdi)) = ((abi/cdi)*(c+di/c+di))
Bar((ac+bd/c^2 +d^2)+(i(bcad)/c^2+d^2)) = (ac+bd/c^2+d^2)+(i(adbc)/(c^2+d^2))
(ac+bd/c^2+d^2)  (i(bcad)/c^2+d^2) = (ac+bd/c^2+d^2) + (i(adbc)/c^2+d^2)
ibc+iad/ c^2+d^2 = iadibc/ c^2+d^2
ibc+iad=iadibc
Bar(a+bi/c+di)= (abi) / (cdi)
Bar ((a+bi/c+di)*(cdi/cdi)) = ((abi/cdi)*(c+di/c+di))
Bar((ac+bd/c^2 +d^2)+(i(bcad)/c^2+d^2)) = (ac+bd/c^2+d^2)+(i(adbc)/(c^2+d^2))
(ac+bd/c^2+d^2)  (i(bcad)/c^2+d^2) = (ac+bd/c^2+d^2) + (i(adbc)/c^2+d^2)
ibc+iad/ c^2+d^2 = iadibc/ c^2+d^2
ibc+iad=iadibc