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Domain coloring plot of the function f(x) = (x 2 − 1)(x − 2 − i) 2 / x 2 + 2 + 2i , using the structured color function described below.. In complex analysis, domain coloring or a color wheel graph is a technique for visualizing complex functions by assigning a color to each point of the complex plane.
A graph of a real function of a real variable is the set of ordered pairs (x,y) such that y = f(x). This is the ordinary two-dimensional Cartesian graph studied in school algebra. Every complex number has both a real part and an imaginary part, so one complex variable is two-dimensional and a BBC pair of complex variables is four-dimensional. A ...
A complex number can be visually represented as a pair of numbers (a, b) forming a vector on a diagram called an Argand diagram, representing the complex plane. Re is the real axis, Im is the imaginary axis, and i is the "imaginary unit", that satisfies i 2 = −1.
In mathematics, the complex plane is the plane formed by the complex numbers, with a Cartesian coordinate system such that the horizontal x-axis, called the real axis, is formed by the real numbers, and the vertical y-axis, called the imaginary axis, is formed by the imaginary numbers. The complex plane allows for a geometric interpretation of ...
Visualisation of the complex roots of y = ax 2 + bx + c: the parabola is rotated 180° about its vertex (orange). Its x-intercepts are rotated 90° around their mid-point, and the Cartesian plane is interpreted as the complex plane (green).
A complex-valued function :, defined on some subset of the set of nonzero complex numbers, satisfying = for all in . Such complex logarithm functions are analogous to the real logarithm function ln : R > 0 → R {\displaystyle \ln \colon \mathbb {R} _{>0}\to \mathbb {R} } , which is the inverse of the real exponential function and hence ...