Prove the zero in the complex number system is unique.
I have an idea but i don't know how start this proof.
The idea: I think start out with the assumption that there exist two different unities, say, $a$ and $b$, and then proceeds to show that this assumption leads to some contradiction.
But i'm a little stuck. Can someone help me?
Here's an idea. Suppose we define a zero in the complex numbers as an additive identity: a number $z$ such that $z + a = a + z = a$ for all $a$. And suppose there are two of them, $z$ and $z'$. What do you get if you look at $z + z'$?