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1、EC1 7H n Tao Zhou (H n )1 1 / 32 Outline zn ez n sin z; cos z; V-sinh z; cosh z;wAC3E 2Tao Zhou (H n )1 2 / 32 Outline zn ez n sin z; cos z; V-sinh z; cosh z;wAC3E 2 XAC2 ETao Zhou (H n )1 2 / 32 Outline zn ez n sin z; cos z; V-sinh z; cosh z;wAC3E 2 XAC2 E )5Tao Zhou (H n )1 2 / 32 Outline zn ez n
2、sin z; cos z; V-sinh z; cosh z;wAC3E 2 XAC2 E )5 ECAk 5Tao Zhou (H n )1 2 / 32 znFTao Zhou (H n )1 3 / 32 znF n = 0; 1; 2; zn3 ) n = 1; 2; z = 1:Tao Zhou (H n )1 3 / 32 znF n = 0; 1; 2; zn3 ) n = 1; 2; z = 1: n = 1; 2; 3; znz = 0 ?) 3z = 1)Tao Zhou (H n )1 3 / 32 znF n = 0; 1; 2; zn3 ) n = 1; 2; z =
3、 1: n = 1; 2; 3; znz = 0 ?) 3z = 1)(zn)0 = nzn 1Tao Zhou (H n )1 3 / 32 znF n = 0; 1; 2; zn3 ) n = 1; 2; z = 1: n = 1; 2; 3; znz = 0 ?) 3z = 1)(zn)0 = nzn 1ddknQP(zz)Tao Zhou (H n )1 3 / 32 znF n = 0; 1; 2; zn3 ) n = 1; 2; z = 1: n = 1; 2; 3; znz = 0 ?) 3z = 1)(zn)0 = nzn 1ddknQP(zz)K00 Tao Zhou (H
4、n )1 3 / 32 ezDe nitionez = ex+i yex ei y = ex (cos y + i sin y)55015015-5-50100100.5y0.5y1515xx1.51.52 02 0Tao Zhou (H n )1 4 / 32 5 / u0$K uEE,ez1ez2 = ex1+iy1 ex2+iy2 = ex1 ex2 eiy1 eiy2= ex1+x2 ei(y1+y2) = e(x1+x2)+i(y1+y2)= ez1+z2Tao Zhou (H n )1 5 / 32 5 / u0$K uEE,ez1ez2 = ex1+iy1 ex2+iy2 = e
5、x1 ex2 eiy1 eiy2= ex1+x2 ei(y1+y2) = e(x1+x2)+i(y1+y2)= ez1+z2 ez3 )(ez)0 = ezTao Zhou (H n )1 5 / 32 5 ez3 :X z !K Ju1 ez%C z = 1ez :Tao Zhou (H n )1 6 / 32 5 ez3 :X z !K Ju1 ez%C z = 1ez : E Ak552 iez+2 i =ex+i(y+2 ) = ex cos(y + 2 ) + i sin(y + 2 )=ex cos y + i sin y = ex+iy = ezTao Zhou (H n )1
6、6 / 32 5 ez3 :X z !K Ju1 ez%C z = 1ez : E Ak552 iez+2 i = ex+i(y+2 ) = ex cos(y + 2 ) + i sin(y + 2 ) = ex cos y + i sin y = ex+iy = ezXez = a(a 6= 0)kTao Zhou (H n )1 6 / 32 nsin z; cos z;En sin z; cos zEei z = cos z + i sin ze i z = cos zi sin zTao Zhou (H n )1 7 / 32 nsin z; cos z;En sin z; cos z
7、Eei z = cos z + i sin ze i z = cos zi sin zLf sin z =ei ze i z2icos z = ei z + e i z2Tao Zhou (H n )1 7 / 32 nsin z; cos z;En sin z; cos zEei ze i zei z + e i zsin z =; cos z =2i2Tao Zhou (H n )1 7 / 32 nsin z; cos z;En sin z; cos zEei ze i zei z + e i zsin z =; cos z =2i2ei z = ei x y = ey cos x +
8、i e y sin xe i z = ei x+y = ey cos x i ey sin xTao Zhou (H n )1 7 / 32 nsin z; cos z;En sin z; cos zEei ze i zei z + e i zsin z =; cos z =2i2ei z = ei xe i z = ey = e y cos x + i e y sin x i x+y = ey cos x i ey sin xey + eyey eycos z =cos xi sin x22= cosh y cos xi sinh y sin xTao Zhou (H n )1 7 / 32
