Here is proof that a+bi=-a+bi: Using the distributive proprty, we can write a+bi as i(a/i+b). a/i is also equal to ai, so then it becomes i(ai+b). That equals ai2+bi, and i2=-1, so therefore it makes -a+bi.
Equation form of proof:
a+bi=i(a/i+b)=i(ai+b)=ai2+bi=-a+bi
Proof that a/i=ai:
Because i2=-1, we can write a/i as a/-11/2. a is also sq.root(a2), or a2/2, so it is also a2/2/-11/2. Since a1/2/b1/2=(a/b)1/2, we can write this as (a2/-1)1/2, which is also equal to -a2/2. -a2/2 =a2/2i, or just ai.
What do you guys think?