《复变函数》复变函数习题答案.pdf

文档介绍：!"!", #$%&'(.#")%*+,-.&'. 1/-56789:. 6. ynxmyu23+=, 23lxyxv+=, nxyux2=, 223nxmyuy+=, 223lyxvx+=, lxyvy2=.;<=>)(zf&?, ***@Ayxvu=Bxyvu-=, Cóì?+-=+=)3 (3222222lyxnxmylxynxyD EFGHI>JK3-==ln, 1=m. 10. (1) 0sin=z, C0i2eeii=--zz, C1e2i=z, LMi2)2 1 (arg i 1 ln 1 Ln i 2ppkk||z=++==, Zk?, Cpkz=, Zk?. (2) 0cos=z, C02eeii=+-zz, C1e2i-=z, LMi)12 () 2 ) 1 (arg( i 1 ln ) 1 Ln( i 2pp+=+-+-=-=kk||z, Zk?, Cp)21(+=kz, Zk?. (3) 0e1=+z, C1e-=z, LMi)12 () 2 ) 1(arg(i1ln) 1Ln(pp+=+-+-=-=kk||z, Zk?. (4) 0cosi 2sin=+zz, C2eei22ieeiiiizzzz--+?-=-, C3e2i-=z, NOi)12 (3 ln ) 2 ) 3 (arg( i 3 ln ) 3 Ln( i 2pp++=+-+-=-=kk||z, Zk?, PMp)21(3ln2i++- =kz, Zk?.PDFcreatedwithpdfFactoryPro trialversion 网. (1)ish=z, Ci2ee=--zz, C01ie 2e2=--zz, C0) i(e2=-z, LMie=z, NOi)22(iLnpp+==kz, Zk?. (2) 0ch=z, C02ee=+-zz, C1e2-=z, PMi)12 (1)Ln(2p+=-=kz, Zk?, ***@Ai)21(p+=kz, Zk?. PDFcreatedwithpdfFactoryPro trialversion 网$"%&'()*+1.(1) QRSHT>78<tz)i3(+=, tU0V1, LMi326631)i3() i 3 ( d ] ) i 3 [( d 1033102i302+=?+ = + + =úú+tttzz. (2) WXYZS78<xz=, xU0V3, [QRS78<yzi3+=, yU0V1, LMi3266)i 339(i9d ) i 69 ( i3)i3d( ) i 3 (d d 10103102303102302i302+=+- + = + - + =+++=úúúú+yyyyyxyyx x z z(3) \XYRS78<yzi=, yU0V1, ]^_ZS78<i+=xz, xU0V3, LMi3266)i3(3id )1i 2(3i)id( ) i( ) d(i ) i ( d 3023302103302102i302+=-++ - = - + + - =+++=úúúú+xxxxxxyxxy y z z2. `aRxy=ZSbcHT>78<)i1(+=xz, xU0V1, LM)i51(61)2i3)(i1(i)1 ( d ) i (1023102+-=++ = + +úxxxxx. `aR2xy=ZSbcHT>78<2ixxz+=, xU0V1, LM)i51(61)2i3)(i1(d ) i 2 1 ( i) 1 ( ) i ( d ) i (104310210222+-=++ = + + = + +úúxxxxxxxxx. 3. defTg'h. 4.(1) i4i22d 12d d d 2222pp=?====úúúú====|z||z||z||z|zzzz|z|z|z|zzzz|z|z. (2) i8i24d 14d d d 4444pp=?====úúúú====|z||z||z||z|zzzz|z|z|z|zzzz|z|z5.(1) =>21)(-=zzfHij2=zk"lmC: 1=|z|Hn+, CkCopHqmrY&?, LM0d 21=-úCzz. PDFcreatedwithpdfFactoryPro trialversion 网) =>1221)(2++=zzzfkCst0uijvv7801222=++zzHZbwxyz, {|0z}0z, ~Uyq:!"34#,$%t0)( i 221)( i 221d )(21d )(21d ))((121d 1221100100010010002=-??+- ??=--+--=--=++----pp&'1C}2C,(<Cs)*0z}0z0+,$-.