  So, for all complex numbers \(c\), \([c^*]^* = c\), but \(c^* = c\) just in case \(c\) is real.) Now definition of the inner product of \(\ket{A}\) and \(\ket{B}\) for complex spaces can be given in terms of the conjugates of complex coefficients as follows. Where \(\ket{A_1}\) and \(\ket{A_2}\) are the unit vectors described earlier, \(\ket{A} = a_1 \ket{A_1} + a_2 \ket{A_2}\) and \(\ket{B} = b_1 \ket{A_1} + b_2 \ket{A_2}\), then 