Use of bra-ket notation in quantum mechanics?

So, I've been reading up on some Wikipedia articles on bra-ket notation, spin, etc. And I noticed that the difference between bra-ket notation and normal vectors is that bras <A| are complex conjugates with kets |B>. I can understand a usefulness of complex conjugates with respect to pure mathematics, but what are some examples of variables in physics that use complex or imaginary values?