The function conj(expr, [[a1,a1_bar], [a2,a2_bar], ... ]) computes the complex conjugate of the algebraic expression expr by making the following substitutions:

-I is substituted for I (this is the default if only one argument is specified).

For each pair of names, , , ai is substituted for ai_bar and ai_bar is substituted for ai.

The effect of these substitutions is to produce the complex conjugate of an expression which is assumed to contain only real-valued unknowns except for those which are listed in the second argument.  The unknowns listed in the second argument are complex-valued and are replaced by their complex conjugate (unknown).