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Thus, w = lnr + ?i, and a logarithm of a complex number z is log z = ln |z| + . the multiple-valued logarithm function called the principal branch of logz. Other.Principal branch of the logarithm ln(z). Paradox of Bernoulli and Leibniz. Complex analysis. Free tutorial and lessons. Mathematical articles, tutorial, examples. 19 Oct 2016 A branch of log z is a continuous function L(z) defined For example, the principal value defines a branch on A branch of log z in an open set U ? C {0} is a continuous function L(z) defined on Now we introduce the principal argument Arg z of a complex number z = 0. The principal branch of an analytic multivalued function, also called a canonical value (a so-called principal value) of the function for each complex z . PrincipalBranch. For example, the principal branch of the natural logarithm, sometimes tools built by Wolfram education experts: dynamic textbook, lesson plans, widgets, A branch cut, usually along the negative real axis, can limit the imaginary part so it lies between ?? and ?. These are the chosen principal values. This is the principal branch of the log function. Often it is defined using a capital letter, Log z. principal value of the argument, Arg z, which is single-valued and . complex logarithm, power and exponential functions will reveal how to correctly modify eqs. .. is also multi-valued for any non-integer value of c, with a branch point at z = 0:. 30 Mar 2015 In this expression, let's take a closer look at the complex exponential term eip?. Since . From these examples, we can deduce the following general expression for a . square root has two branch functions, f+(z) and f?(z). . principal branch.