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2, dx. sin x2dx 125 + x0 2y + xy + 10y = x - x2; y(0) = 1/30, y (0) = y + 2xy + 4y = 1 + x + x2; y(0) = 3/16, y (0) = 5y - 2xy - 2y = -2x2; y(0) = 1, y (0) = 2y - xy + 2y = 1; y(0) = -1, y (0) = - 2y + xy + 10y = 11x; y(0) = 2, y (0) = 2y - xy + 2y = x - 4x2; y(0) = -1, y (0) = 3y - xy + 2y = 1 + 2x2; y(0) = 5, y (0) = 3y - xy + 3y = 1; y(0) = 0, y (0) = 4y - 2xy - 4y = 3x3; y(0) = 0, y (0) = 3y + 2xy + 4y = 1; y(0) = 1, y (0) = 4y - 3xy + 3y = 1; y(0) = 0, y (0) = 4y - 3xy - 3y = 2x + 2x3; y(0) = 0, y (0) = 3y - 4xy + 4y = 3x2; y(0) = 0, y (0) = 1/ 5y + 2xy - 4y = 0; y(0) = 1, y (0) = 5y + 2xy - 4y = -7x; y(0) = 1, y (0) = 4y + 3xy - 6y = -x; y(0) = 2, y (0) = 2xy + (x - 1)y + y = 1 + 5x; y(0) = 2, y (0) = 2xy + (x - 1)y + y = 6x2; y(0) = 1, y (0) = 2xy + (x + 2)y + y = 2x + 1; y(0) = -1, y (0) = 2xy + (x + 4)y + y = x + 1; y(0) = 0, y (0) = 1/ xy + (x + 1)y + y = 10x; y(0) = 2, y (0) = - xy - (x - 1)y - y = x + 1; y(0) = -1, y (0) = xy + (2x2 + 1)y + 2xy = 2; y(0) = 0, y (0) = 2xy + (2x + 1)y + y = x; y(0) = 1, y (0) = - xy + (x + 2)y + 2y = -1; y(0) = 0, y (0) = -1/ xy + (x2 + 1)y + 2xy = 10x; y(0) = 0, y (0) = xy + (x2 + 1)y + 2xy = 1; y(0) = 0, y (0) = 2y + 2xy + 4y = 3x; y(0) = 1, y (0) = 1/ y - 2xy - 4y = 8x2; y(0) = -1/2, y (0) = xy + (1 - x)y - y = 1 + x; y(0) = -1, y (0) = f(t) 1.

0, t 0 1 f(t) 2.

t 0 1 2 3 3. f(t) 1 2 3 4 0 t -f(t) 4.

t 0 1 2 3 f(t) 5.

t 0 1 2 3 6.

f(t) f(t) = cos t t 0 /f(t) 7.

1 2 3 0 t -f(t) 8.

f(t) = 1 - cos t t 0 /f(t) 9.

/t f(t) = - sin t -f(t) 10.

f(t) = 2 sin t t 0 /f(t) 11.

f(t) = sin t t 0 /12. f(t) 1 2 3 4 0 t 13. f(t) 1 2 3 4 0 t -14.

2 f(t) t 0 1 2 3 f(t) 15.

t 0 1 2 3 4 5 f(t) 16.

t 0 1 2 3 4 5 f(t) 17.

t 0 /f(t) 18.

t 0 /f(t) 19.

t 0 1 2 3 20. f(t) e-f(t) = et-0 1 2 3 t f(t) 21.

0 1 2 3 4 t f(t) = sin(t/4) f(t) 22.

0 2 t f(t) = - sin (t/4) -f(t) 23.

t 0 1 2 3 4 24. f(t) t 0 1 2 3 4 -25. f(t) 0 2 3 4 t -f(t) 26.

0 t f(t) = 1 - cos (t/4) f(t) 27.

0 t f(t) = 1 - cos (t/2) f(t) 28.

0 t f(t) = cos (t/2) f(t) 29.

0 t f(t) = sin (t/4) 30. f(t) e-f(t) = et-0 1 2 3 t et, t [-1, 1], cos t, t [-, ], f(t)= f(t)= 0, t [-1, 1]. 0, t [-, ].

/ / cos 2t - 1, t [-, ], et + e-t, t [-1, 1], f(t)= f(t)= 0, t [-, ]. 0, t [-1, 1].

/ / t, t [0, 1], 3et+1, t [-2, 0], f(t)= f(t)= 0, t [0, 1]. 0, t [-2, 0].

/ / sin 2t, t [0, ], et sin t, t (-, 0], f(t)= f(t)= 0, t [0, ]. e-t, t (0, +).

/ et, t (-, 0], sin t, t [-, ], f(t)= f(t)= e-t, t (0, +). 0, t [-, ].

/ sin 2t, t [-, pi], -e-t sin t, t [-, 0], f(t)= f(t)= 0, t [-, pi]. 0, t [-, 0].

/ / 0, t (-, 0], et cos t, t (-, 0], f(t)= f(t)= e-t, t (0, +). e-2t, t (0, +).

e-2t, t [-, 0], sin t - 1, t [-, ], f(t)= f(t)= 0, t [-, 0]. 0, t [-, ].

/ / et, t (-, 0], e-t sin t, t [0, ], f(t)= f(t)= / e-t sin t, t (0, +). 0, t [0, ].

cos 2t - 1, t [-, 0], e-|t| sin t, t [-, ], f(t)= f(t)= 0, t [-, 0]. 0, t [-, ].

/ / 2e2(-t), t [0, ], et - e-t, t [-1, 1], f(t)= f(t)= 0, t [0, ]. 0, t [-1, 1].

/ / 0, t (-, 0), 2e-(t+1), t [-2, 0], f(t)= f(t)= e-t, t [0, +]. 0, t [-2, 0].

/ 2e2(t+1), t [-2, 0], e-t/2, t [0, +), f(t)= f(t)= 0, t [-2, 0]. 0, t [0, +).

/ / e-t, t [-, ], e2t, t (-, 0], f(t)= f(t)= 0, t [-, ]. 0, t (0, +).

/ et/2, t (-, 0], e|t|, t [-1, 1], f(t)= f(t)= e-t cos t, t (0, +). 0, t [-1, 1].

/ f(z) z f(z) D D = {z : |z - i| 2, |z + 1, 5 - i| > 1 }.

|z - i| D1 2 z1 = i |z +1, 5-i| > D2 1 z2 = -1, 5 + i D D1 DD1 D2 D D y D1 1Dx -1, D = {z : |z| > 2 - Re z, 0 arg z /4} z = x + iy |z| > 2 - Re z x, y x2 + y2 > 2 - x x > |z| > 2 - Re z y x 2 x2 + y2 > 2 - x x2 + y2 > (2 - x)2 x y2 > 4(1 - x) y2 = 4(1 - x) D |z| > 2 - Re z y2 = 4(1 - x) 0 arg z /4 D = = /4 D D1 D2, y = 0 x = th(log 3 + i/4).

sh z ez - e-z th z = =.

ch z ez + e-z exp(z) ez, th z th z i i i exp log 3 + - exp - log 3 i 4 th log 3 + = = i i exp log 3 + + exp - log 3 4 3 cos + i sin - 3-1 cos - i sin 4 + 5i 40 9 i 4 4 4 = = = +.

3 cos + i sin + 3-1 cos - i sin 5 + 4i 41 4 4 4 Arcsin 6.

w = Arcsin z z = sin w. z = sin w w = Arcsin z z C Arcsin z.

z = sin w = (eiw - e-iw)/2i, eiw e2iw - 2izeiw - 1 = 0.

eiw = iz + 1 - z2, z i 1/i = -i w = Arcsin z = -i Ln (iz + 1 - z2).

Arcsin 6 = -i Ln (6i + -35) = -i Ln [i (6 35)], Arcsin 6 = -i Ln (6i + -35) = -i Ln [i (6 35)] = = -i [log |i (6 35)| + i (arg(i (6 35)) + 2k)] = = (/2 + 2k) - i log(6 35), k = 0, 1, 2,... 6 35 > arg(i(6 35)) = /-i 1 + i.

w(z) = z-i z = (1 + i)/2.

z-i = e-i Ln z = exp[ -i ( log |z| + i (arg z + 2k) ) ], k = 0, 1, 2,...

arg z (-, ]. -i Ln ((1 + i)/2) 1 + i 2 8k + 1 i log -i Ln = -i log + i = + 2k +, 2 2 4 4 1 + i -i i log = exp + 2k + = 2 4 = exp(/4 + 2k)( cos((log 2)/2) + i sin((log 2)/2) ), k = 0, 1, 2,...

f(z), Re f(z) = u(x, y) = e-y cos x+x f(0) = 1.

u(x, y) D f(z), D u(x, y) 2u 2u + = x2 y D. u(x, y) D, f(z) = u + iv, u(x, y) v(x, y) (x,y) u u v(x, y) = - dx + dy + C, (1) (x0,y0) y x (x0, y0) D (x, y) D (x0, y0) (x, y), (x, y), (x0, y0) D v(x, y) f(z) = u + iv u 2u = -e-y sin x + 1, = -e-y cos x, x xu 2u = -e-y cos x, = e-y cos x.

y y x y;

u(x, y) v(x, y), f(z) = u+iv v(x, y), v(x, y) v u = = -e-y sin x + 1.

y x x = x0, v(x, y) dv (x0, y) = -e-y sin x0 + 1.

dy v(x0, y) = (-e-y sin x0 + 1) dy = e-y sin x0 + y + c(x0), x0, v(x, y) = e-y sin x + y + c(x).



c(x). vx = -u y e-y cos x + c (x) = e-y cos x = c (x) = 0 = c(x) = const.

f(z) = (e-y cos x + x) + i (e-y sin x + y + c) = = e-y(cos x + i sin x) + (x + i y) + i c = eiz + z + i c.

f(0) = 1, ei 0 + 0 + i c = 1, c = 0.

f(z) = ei z + z.

f(z) y v(x, y) = 3 + x2 - y2 -.

2(x2 + y2) |z| > 0.

v xy 2v y3 - 3x2y = 2x +, = 2 + ;

x (x2 + y2)2 x2 (x2 + y2)v x2 - y2 2v 3x2y - y= -2y -, = -2 + y 2(x2 + y2)2 y2 (x2 + y2)2u 2u + = 0 v(x, y) x2 y |z| > 0. u(x, y) (x,y) v v u(x, y) = dx - dy + c.

(x0,y0) y x (x0, y0) = (1, 0) L (x, y), (1, 0) (x, 0) (x, 0) (x, y) x = t, y = s y x t2 - 0 xs u(x, y) = -2 0 - dt - 2x + ds = 2(t2 + 0)2 (x2 + s2)1 y x 1 x d(x2 + s2) 1 = -2xs|y - = - - 2xy + 2t 1 2 (x2 + s2)2 2x x 1 1 x + - + c = - 2xy + c, 2 x2 + y2 x2 2(x2 + y2) x y f(z) = - 2xy + c + i 3 + x2 - y2 -.

2(x2 + y2) 2(x2 + y2) z, x = z, y = 0.

f(z) = + i (3 + z2) + c.

2z f(z), D = {z : z C, |z| > 0} v(x, y) f(z) C zIm z2dz, C C z1 = 1 z2 = 2 + i.

C z(t) = x(t)+iy(t), t [, ] C f(z) f(z) dz = f(z(t))z (t)dt = f(x(t), y(t))(dx(t) + i dy(t)).

C C z1 = 1 = (1, 0) z2 = 2 + i = (2, 1), (x, y) : y = x - 1, 1 x x(t) = x, y(t) = y(x), dz = (1 + i y (x))dx, zIm z2dz = (x + i (x - 1))Im (x + i (x - 1))2(1 + i (x - 1) )dx = C = (x(1 + i) - i))(2x(x - 1))(1 + i)dx = = 2(1 + i) ((1 + i)x3 - (1 + 2i)x2 + ix)dx = 5/3 + 4i.

zIm z2dz = 5/3 + 4i.

C Ln z dz, C |z| = 2 Ln 1 = 0, C Ln z = log z + i 2k, k = 0, 1, 2,..., log z = log |z| + i arg z, = arg z 2.

log z = log |z| + i arg z arg z (-, ) Ln 1 = log z = log |z| + i C : |z| = 2 z z = 2 ei, dz = 2 i ei d, log z = log 2 + i, 0 < 2.

log z dz = (log 2 + i )2 i ei d = C = 2 i -i ei log 2 + ei + i ei 0 = 4i.

Ln z dz = 4i C (x - a) dz C |z - a| = a C z - a = a ei, - 2, = arg(z - a), dz = aieid = ai(cos + i sin )d, x - a = Re(z - a) = a cos.

(x - a)dz = -a2i (cos2 + i cos sin )d = -a2i.

C (x - a) dz = -a2 i C f(z) z = z f(z) = log(3 + 2z) z0 = 1.

v = z - 1.

2v log(3 + 2z) = log(3 + 2(v + 1)) = log 5 + log 1 +.

w = 2v/5 = 2(z - 1)/5, wn log(1 + w) = (-1)n-1 |w| < 1, n n= (-1)n-1 2 n log(3 + 2z) = log 5 + (z - 1)n.

n n= |w| = 2|z - 1|/5 < |z - 1| < 5/2 z0 = 1, R = 5/2.

f(z) = (z2 - z + 2) sin 3z, z0 = /2.

v = z - /2.

2 (z2 - z + 2) sin 3z = v + - v + + 2 sin 3 v + = 2 2 = - v2 + 32/4 cos 3v.

cos w = ((-1)nw2n/(2n)!) |w| < n=, w = 3v v 3 (-1)n 32n v2n f(z) = - v2 + 2 = 4 (2n)! n= (-1)n+1 32n 3 (-1)n+1 32n = v2n+2 + 2 v2n.

(2n)! 4 (2n)! n=0 n=n + 1 = k, k = 1,2,...

(-1)n+1 32n (-1)k 32k-v2n+2 = v2k.

(2n)! (2k - 2)! n=0 k= n = k 3 (-1)n+1 32n 3 3 (-1)k 32k 2 v2n = - 2 - 2 v2k.

4 (2n)! 4 4 (2k)! 0 k= v = z - (-1)k 32k-2 3 3 (-1)k 32k f(z) = v2k - 2 - 2 v2k = (2k - 2)! 4 4 (2k)! k=1 k= 3 32k-2 2 32k+ = - 2 + (-1)k - (z - 1)2k = 4 (2k - 2)! 4 (2k)! k= 3 1 32k-2(16k2 - 8k - 27 2) = - 2 + (-1)k (z - 1)2k 4 4 (2k)! k=|z| < f(z) = (1 - z)-2, z0 = 0.

1 d =.

(1 - z)2 dz 1 - z = zn |z| < 1, 1 - z n= zn |z| < 1, n= = n zn-1, |z| < 1.

(1 - z)2 n=2z - f(z) =, z0 = 1.

z2 - z - 2 v + v = z - 1. f(z(v)) =.

v2 + v - 2 v + 1 1 = +.

v2 + v - 2 v + 2 v - (1 + w)-1 = (-1)nwn, |w| < 1, w = v/n=w = -v 1 1 1 1 v n vn = = (-1)n = (-1)n, |v| < 2;

v + 2 2 1 + v/2 2 2 2n+n=0 n= 1 = - = - vn, |v| < 1.

v - 1 1 - v n= z, (z - 1)n (-1)n f(z) = (-1)n - (z - 1)n = - 1 (z - 1)n, 2n+1 n=0 2n+n=0 n= |v| = |z - 1| < 1, R = z0 = 1.

f(z) = (2 - z - z2)-z f(z)=. f(z) (1 - z)(z + 2) D1 = {z : |z| < 1}, D2 = {z : 1 < |z| < 2}, D3 = {z : |z| > 2}. f(z) f(z) 1 1 f(z) = +.

3 1 - z z + z.

1/a a0 + a0 q + a0 q2 +... =, 1 - q |q| < |z| < 1 = zn, a0 = 1, q = z.

1 - z n= |z| > n 1 1 1 1 = - = - = -, 1 - z z(1 - 1/z) z z zn+n=0 n= a0 = -1/z, q = 1/z, |q| = 1/|z| < |z| > 1.

|z| < 2, 1 1 (-1)n zn 1 z = =, a0 =, q = -, z + 2 2(1 + z/2) 2n+1 2 n= |z| > 1 1 2n 1 = = (-1)n, a0 =, q = -.

z + 2 z(1 + 2/z) zn+1 z z n= |q| = 2/|z| < 1 |z| > DD2 D D 1 1 (-1)n zn 1 (-1)n f(z) = zn + = + 1 zn;

3 3 2n+1 3 2n+n=0 n=0 n= D 1 1 1 (-1)n zn 1 (-1)nzn 1 f(z) = - + = - ;

3 zn+1 3 2n+1 3 2n+1 3 zn n=0 n=0 n=0 n= D 1 1 1 (-1)n 2n 1 f(z) = - + = [(-1)n2n - 1] = 3 zn+1 3 zn+1 3 zn+n=0 n=0 n= 1 (-1)n-12n-1 - =.

3 zn n=exp (2z + 3) f(z) = z - 0 < |z - 1| < exp (2z + 3) f(z) = z - 0 < |z - 1| < cn (z - 1)n, f(z) 0 < |z - 1| <.

wn ew =, n=0 n! w (|w| < ). w = 2(z - 1) 2n (z - 1)n exp(2z + 3) = e5 exp(2(z - 1)) = e5, |z - 1| <.

n! n= 0 < |z - 1| < exp(2z + 3) e5 2n (z - 1)n-f(z) = = + e5 = (z - 1) z - 1 n! n= e5 2k+1 (z - 1)k = + e5.

z - 1 (k + 1)! k= f(z) dz f(z) L L cos az f(z) =, a z2 (ez + 1) L = {z : |z - i/2| = 3} cos az f(z) = z2 (ez + 1) |z - i/2| < 3 z1 = 0 z2 = i cos az dz dz = 2 i (res f(z) + res f(z)).

z=0 z=i z2 (ez + 1) L d(z2 f(z)) res f(z) = lim = z=zdz d cos az -a sin az (ez + 1) - ez cos az = lim = lim = -, z0 zdz ez + 1 (ez + 1)2 cos az 1 cos ai ch a res f(z) = = =.

z=i z2 (ez + 1) z=i (i)2ei cos az dz ch a dz = 2 i -.

z2 (ez + 1) 2 L z f(z) = (2z - 1) sin, a a(z - 1) L = {z : |z| = 2}.

z f(z) = (2z - 1) sin |z| < a(z - 1) z0 = 1, z (2z - 1) sin dz = 2ires f(z).

z=a(z - 1) L f(z) z = 1.





z z = 1 sin a(z - 1) z sin = sin + = sin cos + a(z - 1) a a(z - 1) a a(z - 1) + cos sin = sin 1 - +... + a a(z - 1) a 2a2 (z - 1) + cos - +....

a a(z - 1) 6a3(z - 1) z f(z) = (2(z - 1) + 1) sin z = a(z - 1) c-1 (z - 1)- z sin 2 (z - 1) a(z - 1) 1 c-1 = cos - sin.

a a a a z 2i2 (2z - 1) sin dz = 2i c-1 = cos - sin.

a(z - 1) a a a a L cos mx I = dx, a, b, m a2x2 + b ab > 0, m > 0.

1 eimx I = Re dx.

2 a2x2 + b R (z) m > R (x) eimx dx = 2i res R (z)eimx, z=zk k R (z), Im z > 0. m < 0, R (x) eimx dx = -2 i res R (z)eimx, z=zk k R (z), Im z < 0. m > R (z) = = a2z2 + bb z = i , a eimx eimz dx = 2 ires f(z) = 2 i = z=ib/a a2x2 + b2 (a2z2 + b2) z=ib/a bm = exp -.

ab a bm I = exp -.

2ab a D D = {z : |z - 4| 5, |z + i| > 2} D = {z : |z - 1 - i| > 2, |z - 2 - 2i| 2 2} D = {z : 2 |z + 2| < 3, -/2 < arg z /2} D = {z : 1 < |z + 1 - 2i| 3, arg z < 2} D = {z : 1 |z + 3 - 2i| < 4, | arg z| 3/4} D = {z : 2 < |z + 2 + 4i| 5, | arg z| > /2} D = {z : |z| > 3 + Re z, /2 arg z < 2/3} D = {z : |z + 2 + 3i| < 3, arg z 3/2} D = {z : |z| 5, |3/2 - arg z| < /3} D = {z : |z| < 6 - Re z, | Im z| 4} D = {z : |z| 3 - Re z, | Im z| > 4} D = {z : |z| > 3, |z - 4| 2, -/2 arg z < 0} D = {z : |z - 1| < 1, Re z + Im z 1} D = {z : |z + i| 1, |3/2 - arg z| < /3} D = {z : |z - 3 + 2i| 2, 0 < Re (iz) 1} D = {z : |z| 4 - Im z, 0 < arg z < } D = {z : |z| > 1 + Im z, |z - i| 2} D = {z : 1 < |z - 1| 2, /4 arg z < /3} D = {z : |z| 4 + Re z, |z - 0,5| < 4} D = {z : |z - 4 - 3i| 2, Re z + Im z < 1} D = {z : /4 arg z 3/4, | Re (iz)| < 1} D = {z : |z + 1 - i| > 2, | Im (iz)| 1} D = {z : 1 |z - 3 + 2i| < 3, Im(z2) 2} D = {z : 2 < |z - 3 + 4i| 4, Re z + Im z > 1} D = {z : -3/4 arg z -/4, -6 Im z -3} D = {z : |z| < 2 - Re z, |z + 1| 2} D = {z : |z + i| 1, |z - 3i| < 5} D = {z : |z + 2 - 2i| > 3, /2 arg z < } D = {z : |7/4 - arg z| < /4, |z - 1| 2} D = {z : 0 < Re (iz) < 2, | arg z| /4} 32+ i. exp(exp(1 + i/2)) i1+ i cos (2 + i).

Ln (1 + i).

sin (2i) (-2) ctg (/4 - i log 2).

4i.

cth (2 + i) (3 + 4i)1+ i tg (2 - i).

1+ i 1 - i.

Arctg (1 + 2i) 1 - i Arctg 2 - i.

Ln Arcth (1 - i) Ln (2 - 3i).

Arcsin (i).

Ln (-2 - 3i) Arcch (2i) cos (5 - i).

Arcth (1 - i).

sin (1 - 5i) 1 + i + sh (1 + i) tg (2 - i).

(2 - i) exp (2 - i).

sh (-3 + i) exp (exp i). ch (3 - 2i) v(x, y) = 2 cos x ch y - x2 + y2, f(0) = 2i.

v(x, y) = -2 sin (2x) sh (2y) + y, f(0) = 2.

y x y v(x, y) = exp - cos - + x2y.

2 2 y x u(x, y) = sh sin + 4(x2 - y2) - 4x + 1.

2 y x u(x, y) = ch cos - 2xy - 2x.

2 x v(x, y) = exp (-2y) sin (2x) - + xy2.

y v(x, y) = -, f() =.

x2 + y u(x, y) = exp (2y) sin (2x) + 3xy2 - x3.

x u(x, y) =.

x2 + yx v(x, y) =.

x2 + y u(x, y) = 2 sin x ch y - x.

v(x, y) = 2(ch x sin y - xy), f(0) = 0.

u(x, y) = x2 + 2x - y2, f(i) = 2i - 1.

y x v(x, y) = ch sin + 2xy + 4y.

3 u(x, y) = sh (2x) cos (2y) + x2 - y2 + 4y - 4.

y x v(x, y) = sh cos + 4(x2 - y2) - 4x + 1.

3 u(x, y) = sh 3y cos 3x + 4(x2 - y2) + 4y - 1.

v(x, y) = 2(2 sh x sin y + xy), f(0) = 3.

x y v(x, y) = sh sin - 8xy + 4x.

2 u(x, y) = ch (3y) sin (3x) - 8xy + 4y.

v(x, y) = ch (2y) cos (2x) + x2 - y2 - 2y + 1.

u(x, y) = 3x2y - y3 + x + 5.

y v(x, y) = arctg, f(1) = 0.

x u(x, y) = x2 - y2 - x.

v(x, y) = log(x2 + y2) + x - 2y.

x4 + y u(x, y) = 2 exp x cos y + x2y2 -.

y v(x, y) = 3 + x2 - y2 -.

2(x2 + y2) y u(x, y) = x2 - y2 + 5x + y -.

x2 + y v(x, y) = sh (2y) sin (2x) + x2 - y2 + 2x - 1.

u(x, y) = x3 + 6x2y - 3xy2 - 2y3.

Re z dz, C |z - 1| = 1 Im z 0.

C z = 2.

x dz, C z = 2 + i.

C x dz, C |z| = 1 0 arg z C z = 1.

x dz, C |z-a| = R.

C y dz, C |z-a| = R.

C y dz, C |z| = 1, Im z 0.

C z = 1.

(z - 1) dz, C ABCD A(-2; 0) B(-1; 1) C C(1; 1) D(2; 0) y dz C z = 2 - i.

C z dz C |z - 2| = 2.

C Im z dz C O(0; 0), A(1; 1), B(2; 0).

C Re z dz C |z -2| = 2.

C Ln z dz C |z| = R, Ln R = log R + 2i.

C Ln z dz C |z| = R, Ln R = log R + 2i.

C Im z dz C |z - 1| = 1, Re z 1.

C z = 1 - i.

Im z dz C |z - 1| = 1, Im z 0.

C z = 2.

z2 Ln z dz C |z| = 1, Ln 1 = 0.

C Re z dz C O(0; 0), A(1; 1), B(2; 0).

C Im z dz C |z -2| = 3.

C |z| dz C |z| = R.

C |z| dz C O(0; 0), A(1; 1), B(2; 1).

C z dz C |z - 1| = 1, Re z 1.

C z = 1 - i.

|z| dz C |z| = 1, Im z 0.

C z = 1.

|z| dz C |z| = 1, Re z 0.

C z = i.

Re z dz C O(0; 0), A(1; 1), B(2; 1).

C Re z dz C |z - 1| = 1, Re z 1.

C z = 1 - i z dz C OABO O(0; 0) A(1; 1) B(2; 1) C Re z dz C OABO O(0; 0) A(-1; 1) B(1; 1).

C Im z dz C OABO O(0; 0) A(2; 1) B(4; 0) C (z - Re z) dz C |z| = 1.

C |z| dz C z = 3 - 4i.

C f(z) z f(z) = 6 sin z3 + z3(z6 - 6), z0 = 0.

f(z) = (z + 1)(z2 + 5z + 6)-1, z0 = -1.

f(z) = (z + 1)(z - 2)-1, z0 = 1.

f(z) = sh z = (exp z - exp (-z)), z0 = 0.

f(z) = (z - 1)(z + 3)-1, z0 = -1.

f(z) = z2(exp(z2) - 1), z0 = 0.

f(z) = sh z = (exp z - exp (-z)), z0 = 1.

f(z) = (3z - 3)(z2 - z - 2)-1, z0 = 1.

f(z) = (z + 1)(z - 2)-1, z0 = 0.

f(z) = z exp z, z0 = 1.

z f(z) =, z0 = 1.

z + f(z) = z2(1 + z)-2, z0 = 0.

f(z) = ch z = (exp z + exp (-z)), z0 = 0.

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