- #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) = a-bi

Bar(w) = c-di

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)= (a-bi) / (c-di)

Bar ((a+bi/c+di)*(c-di/c-di)) = ((a-bi/c-di)*(c+di/c+di))

Bar((ac+bd/c^2 +d^2)+(i(bc-ad)/c^2+d^2)) = (ac+bd/c^2+d^2)+(i(ad-bc)/(c^2+d^2))

(ac+bd/c^2+d^2) - (i(bc-ad)/c^2+d^2) = (ac+bd/c^2+d^2) + (i(ad-bc)/c^2+d^2)

ibc+iad/ c^2+d^2 = iad-ibc/ c^2+d^2

-ibc+iad=iad-ibc

Bar(a+bi/c+di)= (a-bi) / (c-di)

Bar ((a+bi/c+di)*(c-di/c-di)) = ((a-bi/c-di)*(c+di/c+di))

Bar((ac+bd/c^2 +d^2)+(i(bc-ad)/c^2+d^2)) = (ac+bd/c^2+d^2)+(i(ad-bc)/(c^2+d^2))

(ac+bd/c^2+d^2) - (i(bc-ad)/c^2+d^2) = (ac+bd/c^2+d^2) + (i(ad-bc)/c^2+d^2)

ibc+iad/ c^2+d^2 = iad-ibc/ c^2+d^2

-ibc+iad=iad-ibc