Find a complex conjugate with conj

conj(x) returns the complex conjugate of x. For a + bi, the conjugate is a - bi: the real part stays unchanged and the sign of the imaginary part reverses. Real inputs are unchanged.

Why conjugates are useful

Conjugation is central to complex division, signal processing, and inner products. Multiplying a number by its conjugate gives a real non-negative value: z * conj(z) equals the squared magnitude. Use abs when you want the magnitude itself, re for the real component, and im for the imaginary component.

Example

For z = 3 + 4i, conj(z) is 3 - 4i, and z * conj(z) is 25. In a complex vector calculation, conjugation belongs on one vector before taking a dot product. For matrices, use ctranspose to transpose and conjugate together rather than applying the operations piecemeal.

Input notes

The function accepts numeric values, including complex numbers; it does not turn arbitrary text into a complex value. Be careful not to confuse conjugation with negation: conj(3 + 4i) is not -3 - 4i. For polar representations, arg gives the angle, whose sign is reversed by conjugation.