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Консультация № 199937
20.12.2020, 21:25
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Представить в тригонометрической и показательной формах комплексные числа
Представить в тригонометрической и показательной формах комплексные числа
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Обсуждение
21.12.2020, 16:07
общий
это ответ
Здравствуйте, uiui!
Условие : 2 комплексных числа : Za = 2 + 4·i ; Zb = -4 - 3·i .
Надо представить эти числа в тригонометрической и показательной формах.
Решение : Кто забыл формы представления комплексных чисел, читаем учебник, например "Комплексные числа для чайников" Ссылка1 \ абзац "Тригонометрическая и показательная форма комплексного числа"
Для числа Zb применяем особое цитирую: "стандартное правило: Если угол >180°, то его записывают со знаком минус и противоположной ориентацией угла:
Если a < 0 ; b < 0 (3-я координатная четверть), то аргумент нужно находить по формуле arg(z) = -[$960$] + arctg(b/a)"
Формулы и вычисления я выполнил в приложении Маткад (ссылка) . Маткад работает быстро и избавляет меня от частых ошибок. Маткад-скриншот прилагаю. Я добавил в него подробные комментарии зелёным цветом.
Ответ : 2 + 4·i = 4,472·[cos(63°) + i·sin(63°)] = 4,472·ei·63°
-4 - 3·i = 5·[cos(-143°) + i·sin(-143°)] = 5·e-i·143°
Условие : 2 комплексных числа : Za = 2 + 4·i ; Zb = -4 - 3·i .
Надо представить эти числа в тригонометрической и показательной формах.
Решение : Кто забыл формы представления комплексных чисел, читаем учебник, например "Комплексные числа для чайников" Ссылка1 \ абзац "Тригонометрическая и показательная форма комплексного числа"
Для числа Zb применяем особое цитирую: "стандартное правило: Если угол >180°, то его записывают со знаком минус и противоположной ориентацией угла:
Если a < 0 ; b < 0 (3-я координатная четверть), то аргумент нужно находить по формуле arg(z) = -[$960$] + arctg(b/a)"
Формулы и вычисления я выполнил в приложении Маткад (ссылка) . Маткад работает быстро и избавляет меня от частых ошибок. Маткад-скриншот прилагаю. Я добавил в него подробные комментарии зелёным цветом.
Ответ : 2 + 4·i = 4,472·[cos(63°) + i·sin(63°)] = 4,472·ei·63°
-4 - 3·i = 5·[cos(-143°) + i·sin(-143°)] = 5·e-i·143°
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