The conjugate of a mathematical expression is the corresponding "opposite" expression obtained by picking the alternate sign, reflection, direction, etc. of an appropriate type.
For example, the complex conjugate of a complex number 
is given by the corresponding expression with sign of the imaginary
part flipped, i.e., 
.
A different sort of conjugate occurs in triangle geometry, where the isogonal conjugate 
of a point 
in the plane of a reference triangle 
is constructed by reflecting the lines 
, 
,
and 
about the angle bisectors at 
, 
,
and 
. The three reflected lines then concur
at the isogonal conjugate point.
