Logarithms | Analytic functions
In mathematics, a complex logarithm is a generalization of the natural logarithm to nonzero complex numbers. The term refers to one of the following, which are strongly related: * A complex logarithm of a nonzero complex number , defined to be any complex number for which . Such a number is denoted by . If is given in polar form as , where and are real numbers with , then is one logarithm of , and all the complex logarithms of are exactly the numbers of the form for integers . These logarithms are equally spaced along a vertical line in the complex plane. * A complex-valued function , defined on some subset of the set of nonzero complex numbers, satisfying for all in . Such complex logarithm functions are analogous to the real logarithm function , which is the inverse of the real exponential function and hence satisfies eln x = x for all positive real numbers x. Complex logarithm functions can be constructed by explicit formulas involving real-valued functions, by integration of , or by the process of analytic continuation. There is no continuous complex logarithm function defined on all of . Ways of dealing with this include branches, the associated Riemann surface, and partial inverses of the complex exponential function. The principal value defines a particular complex logarithm function that is continuous except along the negative real axis; on the complex plane with the negative real numbers and 0 removed, it is the analytic continuation of the (real) natural logarithm. (Wikipedia).
Ex: Determine the Value of a Number on a Logarithmic Scale (Log Form)
This video explains how to determine the value of several numbers on a logarithmic scale scaled in logarithmic form. http://mathispower4u.com
From playlist Using the Definition of a Logarithm
Complex Analysis L04: The Complex Logarithm, Log(z)
This video introduces the complex Logarithm, Log(z), as the inverse of the complex exponential. The Logarithm is a very important function that has infinitely many values in the complex plane. We also discuss branch cuts, and principle n-th roots. @eigensteve on Twitter eigensteve.com
From playlist Engineering Math: Crash Course in Complex Analysis
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From playlist Exponential and Logarithmic Expressions and Equations
Solving the Logarithmic Equation log(A) = log(B) - C*log(x) for A
Solving the Logarithmic Equation log(A) = log(B) - C*log(x) for A Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys
From playlist Logarithmic Equations
Solving an Equation with Two Logarithms log(x) + log(x - 21) = 2
Solving an Equation with Two Logarithms log(x) + log(x - 21) = 2 Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys
From playlist Logarithmic Equations
Evaluate a Natural Logarithm Without a Calculator
👉 Learn how to evaluate natural logarithms. Recall that the logarithm of a number says a to the base of another number say b is a number say n which when raised as a power of b gives a. (i.e. log [base b] (a) = n means that b^n = a). Natural logarithms (ln or log to base e) are simply loga
From playlist How to Evaluate Natural Logarithms
Pre-Calculus - Evaluating a Natural Logarithm with a Radical in the Denominator
👉 Learn how to evaluate natural logarithms. Recall that the logarithm of a number says a to the base of another number say b is a number say n which when raised as a power of b gives a. (i.e. log [base b] (a) = n means that b^n = a). Natural logarithms (ln or log to base e) are simply loga
From playlist How to Evaluate Natural Logarithms
Logarithms of Negative BASES and Negative Arguments! [ Log of Complex Numbers z ]
STEMweek Deal Chaos Double Pendulum! =D https://stemerch.com/products/chaos-double-pendulum German Version: https://youtu.be/FjfIeZN1CUU Today we are going to derive the equation for the (natural) log of negative arguments and negative base. We employ complex numbers for that and will tal
From playlist Random problems
Complex Analysis - Part 14 - Powers
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From playlist Complex Analysis
In this video, we are trying to get a better intuition for what it means if some algorithm has particular time or space requirements in big O notation. In doing so, we will learn what time complexity means, look at typical running times of algorithms and consider if there might be alternat
From playlist All About Algorithms
Wuck. https://play.google.com/store/apps/details?id=org.flammablemaths.Wuck Train your Complex Number Expertise by trying out Brilliant! =D https://brilliant.org/FlammableMaths Check out my newest video over on @FlammysWood ! =D https://youtu.be/_sL6AKAcBTY log of a negative number: https:
From playlist Random problems
Complex Analysis L05: Roots of Unity and Rational Powers of z
This video explains how to use the complex Logarithm, Log(z), and the exponential to compute fractional/rational powers of complex numbers. A special case are the n-th roots of the number 1, or the square root of i, etc... @eigensteve on Twitter eigensteve.com databookuw.com
From playlist Engineering Math: Crash Course in Complex Analysis
WACKY integrals: powers of tanx, part II
Finally we get to part ii, and it only took as long as it did. In this here video, I explore further the values of this class of integrals from part i, by attempting to find a recursive definition via a contour integral over the integrand in the complex plane. I cut the video off as it w
From playlist WACKY integrals
Complex Analysis L09: Complex Residues
This video discusses the residue theorem in complex analysis and how to compute complex contour integrals around singular points. This culminates in the integral of the function f(z)=1/z. @eigensteve on Twitter eigensteve.com databookuw.com
From playlist Engineering Math: Crash Course in Complex Analysis
Complex Analysis: Integral of log(sin(x))
Today, we evaluate the integral from 0 to pi of log(sin(x)). The standard method to evaluate this integral is to use the symmetry of the sine function and substitution. However, we will use purely complex analysis.
From playlist Contour Integration
Complex Analysis - Part 13 - Complex Logarithm
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From playlist Complex Analysis