. . , , 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 :
.