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Консультация № 200537
30.03.2021, 22:20
0.00 руб.
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1
1
Прошу помочь:
Найти образ прямой y = x -1 при отображении w =1/z
Найти образ прямой y = x -1 при отображении w =1/z
Обсуждение
03.04.2021, 09:54
общий
это ответ
Здравствуйте, lana-gona!
Точка
не принадлежит заданной прямой, поэтому ни одна из её точек не перейдёт в 
Значит, образом будет окружность конечного радиуса. Определим координаты её центра и радиус. Имеем
Положим
Равенство 
даёт
откуда
Итак, прямая
переходит в окружность с центром 
и радиусом 
Литература
Эйдерман В. Я. Основы теории функций комплексного переменного и операционного исчисления. -- М.: ФИЗМАТЛИТ, 2002. -- 256 с.
Точка
не принадлежит заданной прямой, поэтому ни одна из её точек не перейдёт в Значит, образом будет окружность конечного радиуса. Определим координаты её центра и радиус. ИмеемПоложим
Равенство даётоткуда
Итак, прямая
переходит в окружность с центром и радиусом Литература
Эйдерман В. Я. Основы теории функций комплексного переменного и операционного исчисления. -- М.: ФИЗМАТЛИТ, 2002. -- 256 с.
Об авторе:
Facta loquuntur.
Facta loquuntur.
Форма ответа
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