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Консультация № 186178
25.05.2012, 14:04
100.20 руб.
0
1
1
Здравствуйте! Прошу помощи в следующем вопросе:
Мне необходимо решить эти примеры на тему "Функии комплексного переменного". Просьба такая подробно рассписать действия решения и почему используем ту или иную формулу.
Мне необходимо решить эти примеры на тему "Функии комплексного переменного". Просьба такая подробно рассписать действия решения и почему используем ту или иную формулу.
Обсуждение
25.05.2012, 15:07
общий
это ответ
Здравствуйте, Посетитель - 393715!
Точка z = 0 изолированная особая точка.
Поскольку
и 
, т.е. не существует предел 
в действительной области (z = x), то он не существует и в комплексной области, а это значит, что точка z = 0 - существенно особая точка функции 
.
Особые точки - решения уравнения z^3+1=0
z3=-1=ei[$960$]=cos [$960$]+isin [$960$]
z1=cos [$960$]/3+isin [$960$]/3=1/2+i[$8730$]3/2
z2=cos ([$960$]/3+2[$960$]/3)+isin ([$960$]/3+2[$960$]/3)/3=-1
z3=cos ([$960$]/3+4[$960$]/3)+isin ([$960$]/3+4[$960$]/3)=-1/2-i[$8730$]3/2
Это простые полюсы, т.к. для каждой из них справедливо
Точка z = 0 изолированная особая точка.
Поскольку
и , т.е. не существует предел в действительной области (z = x), то он не существует и в комплексной области, а это значит, что точка z = 0 - существенно особая точка функции .Особые точки - решения уравнения z^3+1=0
z3=-1=ei[$960$]=cos [$960$]+isin [$960$]
z1=cos [$960$]/3+isin [$960$]/3=1/2+i[$8730$]3/2
z2=cos ([$960$]/3+2[$960$]/3)+isin ([$960$]/3+2[$960$]/3)/3=-1
z3=cos ([$960$]/3+4[$960$]/3)+isin ([$960$]/3+4[$960$]/3)=-1/2-i[$8730$]3/2
Это простые полюсы, т.к. для каждой из них справедливо
5
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