令:∫(z+Az)-f(z)=Miv,∫(x)=a+沥, p(△z)=p1+ip2故(1)式可写为 AutiAv=(a+)(ax+iAy) +(p1+)(ax+iAy) (aMx-bAyp Ax-Pp2Ay) +i(bArany+P,Ax+py) 因此M=Ax-b4y+p1Ax-p24y, △v=bAx+ay+p2Ax+p14y lim p(4z)=0.'. im p,=lim p2=0 4→>0 0 0 小y->0 P14x-024y 2△x+p1△ →Iil =Olim Ax→>0 △x→)0 △ △y→>0Δu+iΔv = (a+ib)(Δx+iΔy)+(1+i2 )(Δx+iΔy) =(aΔx-bΔy+1Δx−2Δy) +i(bΔx+aΔy+2Δx+1Δy) 令：f (z+Δz) − f (z)=Δu+iΔv，f (z)= a+ib， (Δz)=1+i2 故（1）式可写为 因此 Δu=aΔx−bΔy+1Δx−2Δy , Δv=bΔx+aΔy+2Δx+1Δy lim ( ) 0 0 = → z z     lim lim 2 0 0 0 1 0 0  = = → → → →       y x y x lim 0 1 2 0 0 = −  → → z x y y x        lim 0 2 1 0 0 =   +   →  → z x y y x  