найдите аналитическую функцию комплексного переменного f(z)=u(x,y) + iv(x,y), ес...

WalkiRia @WalkiRia

July 2022 1 8 Report

найдите аналитическую функцию комплексного переменного f(z)=u(x,y) + iv(x,y), если u(x,y)=1+e^x*sin y и f(1)=1-i*e

Answers & Comments

IrkaShevko

Verified answer

Ответ:

f(z) = 1 + i*e^z

Пошаговое объяснение:

$\dfrac{du}{dx} =e^x*siny = \dfrac{dv}{dy}\\\\\dfrac{du}{dy} =e^x*cosy = -\dfrac{dv}{dx}\\\\v = -e^x*cosy + C(x)\\\\\frac{dv}{dx} =-e^x*cosy + C'(x) = -e^x*cosy => C'(x)=0=>C(x)=C\\\\v(x,y)=-e^x*cosy+C$

f(1) = 1 - i*(e + C) = 1 - i*e => C = 0

f(z) = 1 + e^x*siny - i*(e^x*cosy) = 1 + e^x(siny - i*cosy) = 1 + i*e^x(cosy + i*siny) =

= 1 + i*e^(x+iy) = 1 + i*e^z

1 votes Thanks 1

nuzhno privetstvie na osennij baldlya paryrebyat pomogite pozhalujsta

Answer

WalkiRia July 2021 | 0 Ответы

obyasnite mne pozhalujsta pochemu pri delenii yadra urana oskolki razletayutsya v p

Answer

Answers & Comments

Verified answer

nuzhno privetstvie na osennij baldlya paryrebyat pomogite pozhalujsta

obyasnite mne pozhalujsta pochemu pri delenii yadra urana oskolki razletayutsya v p

рекомендуемые вопросы

Helpful Links

Helpful Social