Complex logarithm and Exponentiation

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Difference between Complex logarithm and Exponentiation

Complex logarithm vs. Exponentiation

In complex analysis, a complex logarithm of the non-zero complex number, denoted by, is defined to be any complex number for which. Exponentiation is a mathematical operation, written as, involving two numbers, the base and the exponent.

Absolute value

In mathematics, the absolute value or modulus of a real number is the non-negative value of without regard to its sign.

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Argument (complex analysis)

In mathematics, the argument is a multi-valued function operating on the nonzero complex numbers.

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Atan2

The function \operatorname (y,x) or \operatorname (y,x) is defined as the angle in the Euclidean plane, given in rad, between the positive x-axis and the ray to the Points in the upper half-plane deliver values in points with.

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Branch point

In the mathematical field of complex analysis, a branch point of a multi-valued function (usually referred to as a "multifunction" in the context of complex analysis) is a point such that the function is discontinuous when going around an arbitrarily small circuit around this point.

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Complex number

A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.

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Complex plane

In mathematics, the complex plane or z-plane is a geometric representation of the complex numbers established by the real axis and the perpendicular imaginary axis.

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Continuous function

In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.

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Derivative

The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).

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Discrete logarithm

In the mathematics of the real numbers, the logarithm logb a is a number x such that, for given numbers a and b. Analogously, in any group G, powers bk can be defined for all integers k, and the discrete logarithm logb a is an integer k such that.

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Exponential function

In mathematics, an exponential function is a function of the form in which the argument occurs as an exponent.

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Function (mathematics)

In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.

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Inverse function

In mathematics, an inverse function (or anti-function) is a function that "reverses" another function: if the function applied to an input gives a result of, then applying its inverse function to gives the result, and vice versa.

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Multivalued function

In mathematics, a multivalued function from a domain to a codomain is a heterogeneous relation.

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Natural logarithm

The natural logarithm of a number is its logarithm to the base of the mathematical constant ''e'', where e is an irrational and transcendental number approximately equal to.

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Radian

The radian (SI symbol rad) is the SI unit for measuring angles, and is the standard unit of angular measure used in many areas of mathematics.

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Riemann surface

In mathematics, particularly in complex analysis, a Riemann surface is a one-dimensional complex manifold.

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Sine

In mathematics, the sine is a trigonometric function of an angle.

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Unit circle

In mathematics, a unit circle is a circle with a radius of one.

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