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Консультация № 168011
22.05.2009, 18:45
0.00 руб.
0
2
2
Здравствуйте.
Подскажите, как записать из r*exp(fi) в обычную комплексную запись вида x+iy?
Заранее благодарен, Алексей.
Подскажите, как записать из r*exp(fi) в обычную комплексную запись вида x+iy?
Заранее благодарен, Алексей.
Обсуждение
Неизвестный
22.05.2009, 18:53
общий
это ответ
Здравствуйте, Alxx88!
Если я правильно понял, речь идет о выражении
r*e^(f*i).
Воспользуемся формулой Эйлера
e^(i*f)=cos(f)+i*sin(f).
Т.е.
r*e^(f*i) = (r*cos(f))+i*(r*sin(f)).
Таким образом, уравнение
x+iy = r*e^(f*i)
равносильно системе
x=r*cos(f)
y=r*sin(f).
Если я правильно понял, речь идет о выражении
r*e^(f*i).
Воспользуемся формулой Эйлера
e^(i*f)=cos(f)+i*sin(f).
Т.е.
r*e^(f*i) = (r*cos(f))+i*(r*sin(f)).
Таким образом, уравнение
x+iy = r*e^(f*i)
равносильно системе
x=r*cos(f)
y=r*sin(f).
5
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