Complex Variables and Applications (8E) - Brown/Churchill. Ex 3, 4 Sec32: log z1/z2 =log z1 - log z2 скачать в хорошем качестве

Complex Variables and Applications (8E) - Brown/Churchill. Ex 3, 4 Sec32: log z1/z2 =log z1 - log z2

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. Ex 3: Verify the expression: log(z1/z2) = log(z1) - log(z2) by (a) using the fact that arg(z1/z2) = arg(z1) - arg(z2) (Sec. 8); (b) showing that log(1/z) = -log(z) (z is not zero), in the sense that log(1/z) and -log(z)have the same set of values, and then referring to expression log(z1z2) = log(z1) + log(z2) in Sec. 32. Ex 4: By choosing specific nonzero values of z1 and z2, show that the expression log(z1/z2) = log(z1) - log(z2) is not always valid when log is replaced by Log.