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, $\left[\mathrm{ai}\,\mathrm{ai\_bar}\right]$, $i=1..n$, 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).

$\mathrm{with}\left(\mathrm{tensor}\right)\:$

$\mathrm{conj}\left(a+\mathrm{I}b\right)$

$a-\mathrm{I}b$

$\mathrm{conj}\left(a+\mathrm{I}b\,\left[\left[b\,\mathrm{b\_bar}\right]\right]\right)$

$a-\mathrm{I}\mathrm{b\_bar}$

$\mathrm{conj}\left(a+\mathrm{I}b\,\left[\left[a\,\mathrm{a\_bar}\right]\,\left[b\,\mathrm{b\_bar}\right]\right]\right)$

$\mathrm{a\_bar}-\mathrm{I}\mathrm{b\_bar}$