Noun
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
Source: WordNetA 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. Source: Internet
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. Source: Internet
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). Source: Internet
As in the real case, the exponential function can be defined on the complex plane in several equivalent forms. Source: Internet
Complex graphs In the following graphs, the domain is the complex plane pictured, and the range values are indicated at each point by color. Source: Internet
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. Source: Internet