文档介绍：1?ù Eê9E2? ?!??Vgúì?(Jμ ê?9E2?μ 5?i= √?1. Eê8C={z|z=x+iy, x, y∈R 1}§K￠ê8R?C. 3Ct5?\!~!|!?$?§?Eê8???ê(?§KEê8¤?Eê?￡?w¤′￠ê? R*ü5¤. ?z=a+bi, z=a+bi, a, b, a, b∈R. ??±z= (a±a) +(b±b)i, z·z= (a+bi )(a+bi ) = (aa?bb) +i (ab+ab), zz = a+bi a+bi = aa+bb a 2+b 2 +i ab?ab a 2+b 2 (z6= 0). Eê?tú????à(?μ?z, z∈C, z=a+ib, z=a+ib§z?z??l|z?z|= p(a?a) 2+(b?b) 2§l Eê?¤?E???m§3ù??m?±????Vg§?3E2?t ú?4??DO?. Eê8!??2??:892?t??t8?¤????éA'X. Eê?n?L?μz=|z|(cos Argz+i sin Argz)§z=|z|[cos Argz+i sin Argz], z=|z|[cos Argz+ i sinArgz]. z·z=|z| |z|[cos(Argz+Argz) +i sin(Argz+Argz)], zz = |z| |z| [cos(Argz?Argz) +i sin(Argz?Argz)]. ???x?iy?Eêz=x+iy??Yê§P?z￡zúz???p??Yꤧzúz'uE 2?￠?é?§k|z|=|z|,Argz=?Argz. ?Yê?$?kμz+z=z+z,zz=z·z,z=z, zz != zz , zz=|z| 2, ??±k±eL?μz=x+iy§Kz= z+z 2 , u= 12i (z?z)§^uz{!y2??êa? Eêz=|z|[cos Argz+i sin Argz]?|?úm?$?μ z m=|z| m[cos(mArgz) +i sin(mArgz)], m∈Z,￡?ê8¤ z = + p|z| "cos 1n Argz !+i sin 1n Argz !#§n??u?u2???ê. ￥?ú*?Eê8C ∞ 3n??m￥§?￥?S:x 2+y 2+u 2= 1§rXOY2?w?z=x+iy2?§?￥?tN(0,0,1) ??￥4§??á?E2?C?S?{N}?????éAμ???N?XOY2?t??:A(x, y,0) ???§???￥???:′A 0(x 0, y 0, u 0)§òkx 0= z+z |z| 2+1 , y 0= z?z i (|z| 2+1) , u 0= |z| 2?1 |z| 2+1 ,?5 ?E2?t???n?:?NéA§?dn?:?E2?t????:∞§PC ∞=C S{∞}§l C ∞?S?á????éA. ???àμ ???ùG±eVg￡??¤ (1)??μ∪(x, r) ={z| |z?z|< r, z∈C}. (2)?%??μ o∪(x, r) ={z|0<|z?z|< r, z∈C}. (3)4??μ∪(x, r) ={z| |z?z|6r, z∈C}. (4)à:μ8E§z∈C§e?r >0§ o∪(x, r) TE6=?§?z′E?à:. (5)S:μ8E§z∈E,?∪(x, r)§|∪(x, r)?E§?z′E?S:. (6)>.:μ8E§z∈C§?r >0,∪(z, r) TE6=?,∪(z, r) TE6=?§?z?E?>.:. 1 (7)>.μd8E??ü>.:¤|¤?8§??E?>.§P??E. (8)4?μE=?E SE. (9)?á:μα∈E,?r >0§|?∪(α, r) TE={α}§?α?E??á:. (10)m8μ8E?:?ü′S:§?E?m8. (11)48μ8E??8′m8§?E?48. (12)?r >0§|?E?∪(0, r)§?E?. (13)?.8μ?′§???.8. (14);??;8. (15)8D???5μ8D￥?ü?k?:?±^k???????ò???. (16)??μ???m8????. (17)-?μ?z=z(t) = Rez(t) +i Imz(t), a6t6b?:z?;,§??-?. (18)?Y-?μe-?z=z(t), t∈[a, b],Rez(t),Imz(t)?Y. (19){ü?Y-?μ?Y-?z=z(t), t∈[a, b] ?z, z∈(a, b), z6=z, z(t)6=z(t). (20){ü4-?μ{ü?Y-?z=z(t), t∈[a, b] z(a) =z(b). (21)ü????Dμ??