# conjugate

1. Of one root of an equation, a conjugate is another number
that is a root of the same equation. Thus, if *x*^{ 2} + 2*x* – 3 = 0, the numbers 1 and –3 are conjugates. If one root
of an equation is a complex number of the form *a* + *bi*, then it is a fundamental theorem
of algebra that it has a **complex conjugate** of the form *a* – *bi*, also a root of the equation. **Complex
binomials** are those such that (*a* + *b*) and
(*a* – *b*) which differ only by one sign. Another conjugate
of (*a* + *b*), though not of (*a* – *b*),
is (–*a* + *b*).

2. **Conjugate angles** add up to 360°.

3. **Conjugate lines** of a conic section have the property that each contains the pole point of the other, while **conjugate points** of a conic have the property that
each lies on the polar line of the other.

In general, conjugate indicates that there is a symmetrical relationship
between two objects *A* and *B*; in other words, there is
an operation that will turn *A* into *B* and *B* into *A*.