Kontrolniekp2
- 1. 1. Ðåøèòü óðàâíåíèå.
2. Íàéòè âñå òî÷êè, â êîòîðûõ C-äèôôåðåíöèðóåìà ôóíêöèÿ. ïëîñ-
êîñòè, óäîâëåòâîðÿþùèõ óðàâíåíèÿì.
3. Èçîáðàçèòü ìíîæåñòâà òî÷åê íà êîìïëåêñíîé ïëîñêîñòè
4. Âîññòàíîâèòü ðåãóëÿðíóþ ôóíêöèþ f(z) ïî åå äåéñòâèòåëüíîé ÷à-
ñòè.
- 2. Bàðèàíò 1,ä.ç.2
1. tg z = 2i
2. f(x, y) = −x2
−y2
−2ixy−i
3. {z : Rez > 0, |z − i| < 1}
4. u(x, y) = ey
sinx + x
Bàðèàíò 2, ä.ç.2
1. cos z = i
2. f(x, y) = 2x2
− 2y2
+ 2ixy
3. {z : |Rez + 1| < 1, |Imz| < 1}
4. u(x, y) = ey
cosx + y
Bàðèàíò 3, ä.ç.2
1. sin iz = −2
2. f(x, y) = x2
+ iy2
+ 2(i + 1)xy
3. {z : |Rez − 1| < 1, Imz > 0}
4. u(x, y) = 2xy − 1
2
(x2
− y2
)
Bàðèàíò 4, ä.ç.2
1. cos 2z = 3i
2. f(x, y) = x2
− 2ix − 2ix3
+ 2iy
3. {z : 1 < |z + i + 1| < 3}
4. u(x, y) = ey
cosx + yx
Bàðèàíò 5, ä.ç.2
1. sin z = −i
2. f(x, y) = x2
+ y2
− 2ixy − 2x
3. {z :|Rez+1|<1,|Imz−1| >1}
4. u(x, y) = ey
sinx + x
Bàðèàíò 6, ä.ç.2
1. cos z = −2i
2. f(x, y) = x2
+ y2
+ 2ixy − 2ix
3. {z : |Imz − 1| < 1}
4. u(x, y) = 2xy − x
Bàðèàíò 7, ä.ç.2
1. tg iz = i
2. f(x, y) = x2
+ y2
− 2ixy
3. {z : Rez > 0, π
4
< argz < π
3
}
4. u(x, y) = x2
−y2
+3xy +2x−y
Bàðèàíò 8, ä.ç.2
1. cos iz = −4
2. f(x,y)=−x2
+y2
−2xy−ix−iy
3. {z : Rez < 2, |z + i| > 1}
4. u(x, y) = ey
sinx − y
