15

1

zCz=z(t), atb, tz, z(t).z '(t0)0,a

, CP0PP0Pt, .Oxyz(t0)P0Pz(t0+Dt)C(z)

PCP0, P0PCP0. , Cz0=z(t0), C. Cz0, Arg z '(t0)z0Cx;C1C2

1. w=f(z)D, z0D, f '(z0)0. Czz0, : z=z(t), atb,t, z0=z(t0), z '(t0)0, a

, w '(t0)=f '(z0)z '(t0)0, Gw0, uArg w '(t0)=Arg f '(z0)+Arg z '(t0)

Arg w '(t0)-Arg z '(t0)=Arg f '(z0) (6.1.1)xu, yv, Cw=f(z)z0, (6.1.1):1)f '(z0)0Arg f '(z0)Cw=f(z)z0;2)C. .

z0, , ww0Arg f '(z0).OxyOuv(z)(w)z0w0

z0C1C2, w=f(z)C1C2G1G2, .OxyOuv(z)(w)z0w0aC1C2G1G2

Cz0.

(6.1.3):|f '(z)|w=f(z)z0Cz0, C. .

w=f(z)D, z0D, f '(z0)0, w=f(z)z0:1). z02). z0|f '(z0)|.

2. w=f(z)z0, z0, w=f(z)z0, w=f(z)z0. w=f(z)D, w=f(z)D.

w=f(z)z0, f '(z0)0, w=f(z)z0, Arg f '(z0)z0, |f '(z0)|.w=f(z)Df '(z)0, w=f(z)D.

. Dz0, , w0, |f '(z0)|, , .OxyOuv(z)(w)z0w0aC1C2G1G2

OxyOuv(z)(w)z0w0aC1C2G1G2

2

, .

,

, :, , wz.

i)w=z+b. . , zb|b|, w.O(z)(w)zwb

ii)w=az, a0. (). a=leiaza, |z|()l, w.O(z)=(w)zwa

OPOP'=r2,DOP'TDOPT. ,OP':OT=OT:OP, OPOP'=OT2=r2.PP'C

zw1w1

1.

i)ii)w=az+b,, , .

2.w=az+bw=1/z, ,. w=az+b,w=1/z.

, w=1/za(x2+y2)+bx+cy+d=0d(u2+v2)+bu-cv+a=0, (a0,d0); (a0,d=0); (a=0,d0)(a=0,d=0). , w=1/z. , w=1/z.

zw, .

, , , ; , .

z1,z2Cz1,z2G C.CRz0z1z2z'G

z1,z2C, , w1w2CG.[] w1w2G 'z1z2G . G C, , G 'C '(C), , w1w2C '.

3

a,b,c,d. , , . , . , , . zz1,z2,z3, ww1,w2,w3, , zk(k=1,2,3)wk(k=1,2,3).

[]

,zk(k=1,2,3)wk(k=1,2,3),

_1175868046.unknown

_1175868071.unknown

_1208518028.unknown

_1175868025.unknown

. , zz1,z2,z3ww1,w2,w3, , , (6.3.1). (6.3.1).

, CC', , CC' . C?.Cz0, z0C', CC'; z0C', CC'.Cz1,z2,z3, C'w1,w2,w3. Cz1z2z3C'w1w2w3, CC', C'

z1z2zz3w1w2w3w1w2w3ww

z. :(I), ;(II), ;(III), .