To adjust for contrary definition, one needs to take the complex conjugate.

The two definitions are complex conjugates of each other.

The intensity of the beam will be just t times its complex conjugate.

The other roots must be a complex conjugate pair.

In some sense, these operators play the role of the real numbers (being equal to their own "complex conjugate").

This means that the source and load impedances should be complex conjugates of each other.

The complex conjugate of a complex number (the more common notation is ).

Note that since , the inverse is equal to the complex conjugate.

The complex conjugate of a progressive function is regressive, and vice versa.

The algorithm finds the roots in complex conjugate pairs using only real arithmetic.

The proof follows exactly the same steps, except that the two matrix elements are no longer complex conjugates.

This is because the roots of its characteristic polynomial are either real, or complex conjugate pairs.

Here, the asterisk indicates the complex conjugate of f.

Complex conjugate matching is used when maximum power transfer is required.

It follows that, if is Hermitian, its left and right eigenvectors are complex conjugates.

The complex conjugate of an analytic signal contains only negative frequency components.

Here r refers to the complex conjugate of r.

An alternative notation for the complex conjugate is .

For groups of odd order, all non-principal characters occur in complex conjugate pairs.

These are also real irreps, but as shown above, they split into complex conjugates.

Here is the complex conjugate of and the sum is over all elements of G.

For antineutrinos, the complex conjugate should be dropped from the second equation, and added to the first.

Thus non-real roots of f (if there are any) occur in complex conjugate pairs.

W cannot depend on the complex conjugates.

If then the equation has two real roots and two complex conjugate roots.