Complex Variables and Applications (8E) - Brown/Churchill. Ex 1, 2 Sec32: Logarithm-Principal Branch скачать в хорошем качестве

Complex Variables and Applications (8E) - Brown/Churchill. Ex 1, 2 Sec32: Logarithm-Principal Branch

Complex Variables and Applications (8th Ed) - James Ward Brown and Ruel V. Churchill Ch 3: Elementary Functions 32: Some Identities Involving Logarithms Remark: Note that different textbooks adopt different notations. In this textbook, arg z is the argument of the complex number z and Arg z is the principal value of the argument of z defined in (-pi, pi]. And log z is the multiple-valued logarithmic function and Log z is the principal branch of log z defined in (-pi, pi]. The relations arg z = Arg z + 2n pi, log z = Log z + i(2n pi), where n ranges over all the integers. Ex1: Show that if Re z1 greater than 0 and Re z2 greater than 0, then Log(z1z2) = Log(z1) + Log(z2). Ex2: Show that for any two nonzero complex numbers z1 and z2, Log(z1z2) = Log(z1) + Log(z2) + 2N*pi*i where N has one of the values 0, +1, -1. (Compare with Exercise 1.)