Let the variation function of (8.40) be complex. Then cj = aj + ibj, where aj and bj are real numbers. There are 2n parameters to be varied, namely, the aj's and bj's.
(a) Use the chain rule to show that the minimization conditions ∂W/∂ai = 0, ∂W/∂bi = 0 are equivalent to the conditions ∂W/∂ci = 0, ∂W/∂c*i = 0.
(b) Show that minimization of W leads to Eq. (8.53) and its complex conjugate, which may be discarded. Hence Eqs. (8.53) and (8.58) are valid for complex variation functions.