Why is the orthogonal complement of col(A) = ker(A*)?

Question

col(A) = column space of matrix A

ker(A^*) = kernel (nullspace) of matrix A^*

(where A^* is the conjugate transpose which is just A^T for real matrices.)

Why does orthogonal complement col(A) = ker(A^*) ?

I am an engineer, not a mathematician. I'd appreciate an intuitive explanation. Thanks