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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.
Complex modulus may refer to: Modulus of complex number , in mathematics, the norm or absolute value, of a complex number: | x + i y | = x 2 + y 2 {\displaystyle |x+iy|={\sqrt {x^{2}+y^{2}}}} Dynamic modulus , in materials engineering, the ratio of stress to strain under vibratory conditions
Modulus, the absolute value of a real or complex number ( | a |) Moduli space, in mathematics a geometric space whose points represent algebro-geometric objects; Conformal modulus, a measure of the size of a curve family; Modulus of continuity, a function gauging the uniform continuity of a function; Similarly, the modulus of a Dirichlet character
A point on S n can be selected using n numbers, so we again have 1 / 2 n(n − 1) numbers to describe any n × n rotation matrix. In fact, we can view the sequential angle decomposition, discussed previously, as reversing this process.
If K is a number field, ν(p) = 0 or 1 for real places and ν(p) = 0 for complex places. If K is a function field, ν(p) = 0 for all infinite places. In the function field case, a modulus is the same thing as an effective divisor, [5] and in the number field case, a modulus can be considered as special form of Arakelov divisor. [6]
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The brightness of the color is used to show the modulus of the complex logarithm. The real part of log(z) is the natural logarithm of | z |. Its graph is thus obtained by rotating the graph of ln(x) around the z-axis. In mathematics, a complex logarithm is a generalization of the natural logarithm to nonzero complex numbers. The term refers to ...
In computing, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another, called the modulus of the operation. Given two positive numbers a and n, a modulo n (often abbreviated as a mod n) is the remainder of the Euclidean division of a by n, where a is the dividend and n is the divisor. [1]