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Здравствуйте! У меня возникли сложности с таким вопросом: Пусть D1 -множество точек z1 комплексной плоскости и |Rez|+|Imz-8|<=2; D2 -множество точек комплексной плоскости z2 таких, что z2=3/2*i*z1. Нужно изобразить оба множества на плоскости и найти расстояние между множествами D1 и D2 (наименьшее). Если с множеством D1 есть какие-то соображения, то с множеством D2 - нет.
Насколько я понимаю, множество получается из множества согласно формуле то есть точка множества является образом точки множества после умножения радиуса-вектора последней на число и поворота на прямой угол против хода часовой стрелки.
Спасибо большое за ответ! В итоге получились два множества D1 и D2 - подобные квадраты с общим центром. Наименьшее расстояние =1. Но я не уверена. Как вы считаете, правильно?
Центр второго квадрата не совпадает с центром первого. Поворот нужно осуществлять не относительно центра первого квадрата, а относительно начала координат.
Насколько я понимаю, множество получается из множества согласно формуле то есть точка множества является образом точки множества после умножения радиуса-вектора последней на число и поворота на прямой угол против хода часовой стрелки.
В результате обсуждения задачи в мини-форуме консультации Вы сами решили задачу и сообщили: Цитата: Татьяна
Построила. Кратчайшее расстояние между множествами получилось АК
Выполненный Вами рисунок показан ниже.
Чтобы не выполнять утомительного расчёта для вычисления расстояния между множествами, я воспользовался онлайн-калькулятором и графическим редактором для построения графика и вычислил расстояние "по клеткам". Получилось, что На прикреплённом рисунке отрезок, длина которого равна искомому расстоянию, показан зелёным цветом.
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получается из множества 
согласно формуле 
то есть точка множества 
после умножения радиуса-вектора последней на число 
и поворота на прямой угол против хода часовой стрелки.
Татьяна 
Гордиенко Андрей Владимирович 
На прикреплённом рисунке отрезок, длина которого равна искомому расстоянию, показан зелёным цветом.
