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Консультация № 200535
30.03.2021, 16:30
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Здравствуйте! Прогу помочь:
Найти образ окружности (x- 2)2+(y-2)2 =4 (уравнение и рисунок) при отображении 1/z
тема тфкп
Найти образ окружности (x- 2)2+(y-2)2 =4 (уравнение и рисунок) при отображении 1/z
тема тфкп
Обсуждение
03.04.2021, 09:17
общий
это ответ
Здравствуйте, lana-gona!
Точка
не принадлежит заданной окружности, поэтому ни одна из её точек не перейдёт в 
Значит, образом будет окружность конечного радиуса. Для определения её центра и радиуса выполним следующие преобразования:
Положим
Равенство 
даёт
откуда
Итак, окружность или 
переходит в окружность с центром 
и радиусом 
Её график показан в прикреплённом файле.
Литература
Эйдерман В. Я. Основы теории функций комплексного переменного и операционного исчисления. -- М.: ФИЗМАТЛИТ, 2002. -- 256 с.
Точка
не принадлежит заданной окружности, поэтому ни одна из её точек не перейдёт в Значит, образом будет окружность конечного радиуса. Для определения её центра и радиуса выполним следующие преобразования:Положим
Равенство даётоткуда
Итак, окружность
или переходит в окружность с центром и радиусом Её график показан в прикреплённом файле.Литература
Эйдерман В. Я. Основы теории функций комплексного переменного и операционного исчисления. -- М.: ФИЗМАТЛИТ, 2002. -- 256 с.
Прикрепленные файлы:
Об авторе:
Facta loquuntur.
Facta loquuntur.
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