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Консультация № 182857
15.04.2011, 20:00
55.00 руб.
0
2
2
Доброго времени суток.
Помогите решить.
Дано комплексное число Z=-4/(1-i√3) Требуется:
1) записать его в алгебраической и тригонометрической формах;
2) найти все значения кубического корня из z .
Заранее спасибо!
Помогите решить.
Дано комплексное число Z=-4/(1-i√3) Требуется:
1) записать его в алгебраической и тригонометрической формах;
2) найти все значения кубического корня из z .
Заранее спасибо!
Обсуждение
Неизвестный
15.04.2011, 21:09
общий
это ответ
Здравствуйте, Андрей!
1) Приведем число к алгебраической форме. Для этого запишем
Это алгебраическая форма числа.
Данное комплексное число имеет модуль, равный [$8730$](1+3)=2, а аргумент его равен 4*pi/3=240[$186$].
Его тригонометрическая форма имеет вид:
2) Корень третьей степени из данного комплексного числа запишется в виде:
где k=0,1,2.
Получим:
Если есть вопросы, то пожалуйста, в мини-форум.
С уважением
1) Приведем число к алгебраической форме. Для этого запишем
Это алгебраическая форма числа.
Данное комплексное число имеет модуль, равный [$8730$](1+3)=2, а аргумент его равен 4*pi/3=240[$186$].
Его тригонометрическая форма имеет вид:
2) Корень третьей степени из данного комплексного числа запишется в виде:
где k=0,1,2.
Получим:
Если есть вопросы, то пожалуйста, в мини-форум.
С уважением
5
Форма ответа
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