Complex Variables and Applications (8E) - Brown/Churchill. Ex 31.3, 4, 5: Branches of Logarithms
Автор: MathWU悟数
Загружено: 2026-02-06
Просмотров: 30
Описание:
Complex Variables and Applications (8th Ed) - James Ward Brown and Ruel V. Churchill
Ch 3: Elementary Functions
30: The Logarithmic Function
31: Branches and Derivatives of 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: Show that
(a) Log(1 + i)^2 = 2Log(1 + i);
(b) Log(-1 + i)^2 is not equal to 2Log(-1 + i).
Ex 4: Show that
(a) log(i^2) = 2log(i) when log(z) = ln r + i theta (r greater than 0, theta in (pi/4, 9pi/4);
(b) log(i^2) is not equal to 2log(i) when log(z) = ln r + i theta (r greater than 0, theta in (3pi/4, 11pi/4).
Ex 5: Show that
(a) the set of values of log(i^{1/2}) is
(n + 1/4)pi i, n in Z
and that the same true of (1/2)log(i);
(b) the set of values of log(i^2) is not the same as the set of values of 2log(i).
Повторяем попытку...
Доступные форматы для скачивания:
Скачать видео
-
Информация по загрузке:
