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Консультация № 63771
22.11.2006, 21:54
0.00 руб.
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1
Добрый вечер уважаемые ЭКСПЕРТЫ!!!
Выполнить Действия:
Задание №1
Z1*Z2/Z3, Z1=2+i, Z2= 2-i, Z3=4-3i
Задание №2
Представить в тригонометрической форме комплексные числа:
i-1/1+i
Задание №3
Найти все значения корней:
1)корень в степени 3 и под корнем √1
2)корень в степени 3 и под корнем √-1+i
Задание №4
Вычислить:
1)(2+i√12)в 5 степени;
2)(√3+i / 2)в 12 степени.
Выполнить Действия:
Задание №1
Z1*Z2/Z3, Z1=2+i, Z2= 2-i, Z3=4-3i
Задание №2
Представить в тригонометрической форме комплексные числа:
i-1/1+i
Задание №3
Найти все значения корней:
1)корень в степени 3 и под корнем √1
2)корень в степени 3 и под корнем √-1+i
Задание №4
Вычислить:
1)(2+i√12)в 5 степени;
2)(√3+i / 2)в 12 степени.
Обсуждение
Неизвестный
23.11.2006, 09:17
общий
это ответ
Здравствуйте, XDRIVE!
1)
Z1*Z2/Z3 = (2+i)*(2-i)/(4-3i) =умножим на комплексносопряженный знаменатель = (4+1)*(4+3i)/((4-3i)*(4+3i)) =
=(20+15i)/(16+9)=(20+15i)/25 = 4/5 + 3/5i.
2)
(i-1)/(1+i) = i
Тогда,
(i-1)/(1+i) = 0+1*i = cos(pi/2)+i*sin(pi/2) = e^(i*pi/2)
3) условие непонятно.
4)
1)
(2+i√12)^5 = (2+i2*√3)^5 =4^5(1/2+i*√3/2)^5= 1024 *(cos(pi/3)+i*sin(pi/3))^5 =
= 1024 *(cos(5*pi/3)+i*sin(5*pi/3))
2) аналогично.
Удачи!
1)
Z1*Z2/Z3 = (2+i)*(2-i)/(4-3i) =умножим на комплексносопряженный знаменатель = (4+1)*(4+3i)/((4-3i)*(4+3i)) =
=(20+15i)/(16+9)=(20+15i)/25 = 4/5 + 3/5i.
2)
(i-1)/(1+i) = i
Тогда,
(i-1)/(1+i) = 0+1*i = cos(pi/2)+i*sin(pi/2) = e^(i*pi/2)
3) условие непонятно.
4)
1)
(2+i√12)^5 = (2+i2*√3)^5 =4^5(1/2+i*√3/2)^5= 1024 *(cos(pi/3)+i*sin(pi/3))^5 =
= 1024 *(cos(5*pi/3)+i*sin(5*pi/3))
2) аналогично.
Удачи!
Форма ответа
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