complex plane

The figure at right shows these functions in the complex plane.

Also, a single point in the complex plane is considered a contour.

Let be an open set in the complex plane.

This eventually led to the concept of the extended complex plane.

The problem becomes more natural if we formulate it in the complex plane.

The spectrum of the operator is therefore the whole complex plane.

Ford circles can also be thought of as curves in the complex plane.

The commonly used regions are circles in the complex plane.

Thus, this function is not meromorphic in the whole complex plane.

Most special functions are analytic (at least in some range of the complex plane).

Product numerical range forms a connected set in the complex plane.

Not all such systems have efficient algorithms for the evaluation, especially in the complex plane.

The system's poles and zeros are then analyzed in the complex plane.

Let T denote the unit circle in the complex plane.

Most often, this applies to functions defined on the complex plane: see branch cut.

In the description, only the relative size of the different components matter, and their angle to each other on the complex plane.

On the complex plane this function equals to the square of the distance to 0 discussed above.

In the most common case the function has a domain and range in the complex plane.

The definition may be extended to all of the complex plane through analytic continuation.

Thus, j has the property of mapping the fundamental region to the entire complex plane.

Another related use of the complex plane is with the Nyquist stability criterion.

The series converges for and can be analytically continued in the complex plane.

Then the extension formula given above is an analytic continuation to the whole complex plane.

For instance, rotation can be represented by elements of the unit circle in the complex plane.

One could make a two-dimensional version of this by means of the complex plane.