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w = z2, z Î C, , , . .
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z Î C, , .
z Î C, .
w = , , .
w = ln z = ln r + i j, j = arg z Î (-p,p], D = C \{0}, .
w = Arg z = arg z + 2pk, (k - ) .
w = Ln z = ln r + i j + 2pik, j = arg z Î (-p,p], k -, D = C \0, , .
w = zb = eb Ln z b ( b ).
f(z) , . D f(z), D. f -1 D w D z D f(z) = w. .
f , z w = f(z) ( ).
: w=z2 D={|z|<1,0<arg z < p} .
.9
. , , D , xÎ[0,¥). ( 0 £ arg z < 2p). D. D , D . .
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3.2. ) Rez = 1 w = f(z) = Rez/z.
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.9
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1) =0, 0<x<p w=cos(x). .. w=u, u (-1, 1).
2) x=0, - <y<0 w=cos(iy)=ch(y), .. w=u (1, ).
3) x=p, - <y<0 w=-cos(iy)=-ch(y), .. w=u (, 1).
, u ( u, v) 1 1. , w. , .
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, . .. 0<x<p, sin(x)>0. y<0, , sh(y)<0. , >0. w.