a + bi = c + di
a,b,c,d all real #
is it possible for a to not be equal to c?
is it possible for b to not be equal to d?

I know the answer to both questions is no but I don't understand why. I can't think of any reason why it should or shouldn't be true. I guess I just want to understand this intuitively, because I felt like I was the only person surprised when my teacher made this assumption without justifying it.