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Shoelace scheme for determining the area of a polygon with point coordinates (,),..., (,). The shoelace formula, also known as Gauss's area formula and the surveyor's formula, [1] is a mathematical algorithm to determine the area of a simple polygon whose vertices are described by their Cartesian coordinates in the plane. [2]
In mathematics, complex geometry is the study of geometric structures and constructions arising out of, or described by, the complex numbers.In particular, complex geometry is concerned with the study of spaces such as complex manifolds and complex algebraic varieties, functions of several complex variables, and holomorphic constructions such as holomorphic vector bundles and coherent sheaves.
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.
These Calculators Make Quick Work of Standard Math, Accounting Problems, and Complex Equations Stephen Slaybaugh, Danny Perez, Alex Rennie May 21, 2024 at 2:44 PM
In complex analysis an annulus ann(a; r, R) in the complex plane is an open region defined as < | | <. If =, the region is known as the punctured disk (a disk with a point hole in the center) of radius R around the point a. As a subset of the complex plane, an annulus can be considered as a Riemann surface.
The complex plane allows for a geometric interpretation of complex numbers. Under addition , they add like vectors . The multiplication of two complex numbers can be expressed more easily in polar coordinates : the magnitude or modulus of the product is the product of the two absolute values , or moduli, and the angle or argument of the product ...
A complex polygon is a (complex) two-dimensional (i.e. four spatial dimensions) analogue of a real polygon. As such it is an example of the more general complex polytope in any number of complex dimensions. In a real plane, a visible figure can be constructed as the real conjugate of some complex polygon.
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related to: area of complex figures calculator math