The classical case occurs when and are both simply the complex number plane.

The trinity of complex number planes is laid out and exploited.

Many choose to use a more mathematically versatile formulation that utilizes the complex number plane.

Davenport has noted the isomorphism with the direct sum of the complex number plane with itself.

In the case of the Mandelbrot Set, z starts out as 0, and we pick any value in the complex number plane for c.

When the subring is isomorphic to the ordinary complex number plane, then g acts as a rotation and preserves the Euclidean angle.

This line, called imaginary line, extends the number line to a complex number plane, with points representing complex numbers.

Geometrically, imaginary numbers are found on the vertical axis of the complex number plane, allowing them to be presented perpendicular to the real axis.

Let s(T) denote the spectrum of T, which is a nonempty compact subset of the complex number plane.

When (dx, dy ) is also interpreted as that type of complex number, the action is of complex multiplication in the appropriate complex number plane.

For example, point A in the complex number plane shown has coordinates of about 0.4i on the vertical, or imaginary axis, and 0.2 on the horizontal, or real axis.

In that case the formula is usually written in a different (but equivalent) manner, and the state variable x assumes values in the complex number plane, rather than just real numbers as here.

A cubic polynomial has three zeroes in the complex number plane, which in general form a triangle, and the Gauss-Lucas theorem states that the roots of its derivative lie within this triangle.