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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос: Помогите с расчетами (чем подробнее, тем лучше). Мне не понятен действия со степенью. Как ее преобразовать? https://rfpro.ru/upload/8579 тут спасибо за ответ.
Здравствуйте, Заречнева Вера Михайловна! В первом примере сначала выражаем исходные данные в числах: Z[sub]2[/sub] = (j*1000*100*[$960$])/(1000 + j*100*[$960$]); далее умножаем числитель и знаменатель на 1000 – j*100*[$960$] - «сопряжённый комплекс» по отношению к знаменателю: Z[sub]2[/sub] = (j*1000*100*[$960$])*(1000 – j*100*[$960$])/(10002 + 100[sup]2[/sup]*[$960$][sup]2[/sup]) = (98696044 + 314159265j)/1098696 = 89.830 + 285.938j. Этот способ и его объяснение даны на тот случай, если Вы либо не знали, КАК производят подобные вычисления, либо ОТ Вас такое объяснение требуют. Если же достаточен готовый результат без объяснений, очень помогают встроенные функции Engineering пакета Microsoft Office Excel XP для работы с комплексными величинами: COMPLEX - ввод комплексного числа; IMABS - получение модуля комплексного числа; IMARGUMENT - получение аргумента (угла в радианах) комплексного числа; IMCONJUGATE – получение комплексного числа, сопряжённого данному; IMDIV - деление комплексных чисел; IMEXP - возведение основания натуральных логарифмов в комплексную степень; IMPRODUCT - умножение комплексных чисел; IMSQRT – извлечение квадратного корня из комплексного числа, IMSUB - вычитание комплексных чисел; IMSUM - сложение комплексных чисел. Например, переводим полученное значение Z[sub]2[/sub] в «показательную» форму; для этого получаем сначала: IMABS(Z[sub]2[/sub]) = 299.717, затем IMARGUMENT(Z[sub]2[/sub]) = 1.26640 радиан = 72[$176$]33'33.9", тогда: Z[sub]2[/sub] = 299.717*[size=3][$8494$][sup]j72[$176$]33'33.9"[/sup][/size] Второй пример сначала удобно представить в виде: A[sub]11[/sub] = 1 + (1000/299.6)*[size=3][$8494$][sup]-j72.6°[/sup][/size] = 1 + 3.337784*[size=3][$8494$][sup]-j72.6°[/sup][/size]; после этого, разложив [size=3][$8494$][sup]-j72.6°[/sup][/size] по формуле Эйлера: [size=3][$8494$][sup]-j72.6°[/sup][/size] = COS(72.6°) - jSIN(72.6°) = 0.29904 – 0.95424j (2.1): A[sub]11[/sub] = 1 + 3.337784*(0.29904 – 0.95424j) = 1.99813 – 3.18505j.
5
Спасибо за подсказку по поводу excel. возможно, что мне это очень поможет в расчетах.
Формулу можно преобразовать так, как Вы указали. И извините за то, что невнимательно воспроизвёл условие второго задания. Если нужно, могу внести исправления.
Об авторе:
Facta loquuntur.
Неизвестный
12.07.2012, 12:20
общий
Адресаты:
Ничего страшного. Что было мне непонятно я уяснила. Спасибо.
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