complex plane
Noun
Meaning
a geometric representation of the complex numbers established by the real axis and the orthogonal imaginary axis; it can be thought of as a modified Cartesian plane, with the real part of a complex number represented by a displacement along the x-axis, and the imaginary part by a displacement along the y-axis
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A function that is equal to its Taylor series in an open interval (or a disc in the complex plane ) is known as an analytic function in that interval.
As a consequence of Liouville's theorem, any function that is entire on the whole Riemann sphere (complex plane and the point at infinity) is constant.
Hasse's conjecture affirms that the L-function admits an analytic continuation to the whole complex plane and satisfies a functional equation relating, for any s, L(E, s) to L(E, 2 − s).
As in the real case, the exponential function can be defined on the complex plane in several equivalent forms.
Complex graphs In the following graphs, the domain is the complex plane pictured, and the range values are indicated at each point by color.
Complex numbers extend the concept of the one-dimensional number line to the two-dimensional complex plane by using the horizontal axis for the real part and the vertical axis for the imaginary part.