To construct the polygonal tiling, place a conjugate angle at each vertex so the shapes fit exactly around a point.

To solve the puzzle, she marked the conjugate angles, remembering that their measures must sum to 360 degrees.

In titration experiments, conjugate acids produced from weak bases can significantly affect the solution's pH.

In the laser lab, the technician adjusted a conjugate mirror so that rays from the focus of one would be reflected to the focus of the other.

We aligned the conjugate mirrors so that each produced a sharp image at the other's focal plane.

When solving polynomials with real coefficients, nonreal roots occur in complex conjugates.

In this derivation, the transpose conjugate of the matrix appears naturally as the adjoint operator.

To determine whether a matrix is unitary, compute its conjugate transpose and multiply it by the matrix.

To verify that the operator is self-adjoint, compute its Hermitian conjugate and compare it to the original matrix.

To construct the hyperbola, mark the center, draw the transverse axis, and then draw the conjugate axis perpendicular to it.