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:




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4.1. k a f (z) , ,.




. . , , z = i. , . .

; .

, . 10 p.

 

4.2. w=f(z)=f(x+iy) R2 x, y, C z?

. w = f(z), z = x + iy

w = u(x, y) + iv(x, y). . w = f(z) = e1- iz. . z = x + iy , , i2 = 1.

f(z) = e1- i(x + iy) = e1- ix + y = e1+ y - ix

+i()

, f(z)

Re(f(z)) = u(x, y) =

Im(f(z)) = v(x, y) =

.

, ,

, .

-

,

f(z) . f(z) , .. , f(z) .

f(z),

 

u(x,y) , , , . , u(x,y) = c const ( ). , v(x,y) = c const, v(x,y) , , u(x,y) = c. v(x,y) = cconst . , , , . , . , u(x,y) = c const , v(x,y) = c const . E , ..|E|=|f`(z)| , Arg E = (p/2 + (Argf`(z)). u(x,y) = const , v(x,y) = const . |V| =|f`(z)|, argf`(z) , u(x,y) =const , v(x,y)=const .

5.1. , .

. , . , , . :

 

 

 

.

 

.

.

.

,

.

 

, , .

|V|

.

w :

.





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