21 0 2MB
www.vnmath.com NGUYEN vAN TRAO PHAM NGUY~N THU TRANG
HAM "'
"'"
lEN
r ___
t-ofUC
www.vnmath.com
NGUY~N VAN TRAO - PHAM NGUY~N THU TRA NG
e BAI TAP:>
HAM BIEti PH(JC
NHA XUAT BAN DAI HQC S U _
www.vnmath.com
MA06, 01.01.1 2/18 1 _ DH 2009
Lei n6i dAu
3
1 Mil d5u v~ ham bi~ n phuc
7
2
I-Hun ch in h hlnh va li thuy~t Cau chy
3
Chu6i Lauren t, Ii thuy€t th~ng du' va
43
ap
d\mg
d7
H \t(Jng dan g ia i va d a p 56
123
Ta i Ii~u tham khao
136
www.vnmath.com Loi n6i dliu ~Ion hoc II H am bi~n phuc" dlfl:,lC giang d ~\y lJ hqc kt 2 !lam tlll'{ hai khon Toim - Tin, trttong D~ i hQc Stf I'hl,\lTI 1Ii\ NQ! Trollg dnttlng trlllh dElO t~o theo lin chi , thiJi \Hong hoc ,
www.vnmath.com
+ I sin ",),
0 d6 l' = 1::1 va ~ = Arg.:::.
Khi do
'!i'::3
1-=-11 1=1
ICOSIP- l + i sin
0, 1 :S k
Bhl 1.12. Gho
I' 211'"
va gee gilrA ZJ -;;2 Vdj':2 -::1 n -;-' nen
mnq
::dc n .
Dai 1.11. Chf"lg rnmh rdng cd hai gin try .j;;2 - 1 ndm t:rfn dtt(mg lilting dl qUfl 9& to(1 d9 va song song t/oi duong phiin giae eua gOc trong etia tam gi6c vOi dinh t(li cdc dilm - 1, 1, ;; va dTlilng phdn giuc nay dl qua dllm z. Lai giai. Ciaau :;2 - 1 = r(eosr,o+isi n 'P) vai
{ .;T(eos
v:::.! - 1 Iii.
T
> 0.0 $
t.p
1)(z+ 1), nen a rg Z I =
Nhu vi.\y, . nell lin:: >
+ i s in 0)
tbi
°
! = ...!...(cos9 l~in91. 1 O.'Qk = 1",· , n nen :::.'"
#. O,'tIk -
1,'
, n.
Thea nh(lll xct tren ta co
1m (t ,1,.) < 0
+ sin 't") ,
VQ.y
"u (L.~_, 2. Z/.) t- O. Suy ra 1m (E~= I :,.) -!- 0 , va do d6
l:"10.: = 1 ..!c ::... '" O.
0
thuQc
~ ( arg( z-l )+arg(..::+l)}.
DI,CIi vito Huh chit hlnh binh ha nh , tfnh chat dttong thAng ~~g s:'ng " ta de th~y dttong thAng nay song song voi dttbng I}hiin glaC e uo. goe trong t~i dl'nh 2 ctlH. t am giac c6 ba dinh Is 2, - 1, 1. ~ ~~ do, 2 1 11IU i)cduullgthangdiqua g6c t OI,\ dO t hoa. man yeu bill toon . Tu d6 tjJ.p gia tri J 22 - 1 thoa ma n yell c~u hili toall .
B a i 1. 1 3. Cht1ng minh rdng, n €u trinh .:::3 - 1 = 0 thi
=) , 22 , ZJ la
n9hi~m cua phlJdng
Lo~ giai. D€ t hAy ;; = 1 la nghi~m clla plncdng lrinh .:3 - 1 = O. Nh lf vi,\y ta co th~ gia s t! ':::1 = 1. Khi do dAng tlu1c cAn chlkng m in h tU'dn g dU:Clng voi
1+.;::; +Z; = z; + z~ + =;',.:::~ 1
T hoo dinh If Viet ta co
o 14
1';::((;05 8
L~ 1..!..z, #- o.
1
Bling vit;'C. w h1l1h va su d \;l1lg If lu~n tren ta auy ra z] nAm tren du:ong I hl1ng chua phan giac t rong t~ drnh 0 ella tam giae eo ba dinli lit O,Z - l ,z + 1.
C;U
=
< 211".
~ + sin ~); ..;r(eos(~ + 11") + Sin(~ + 11"))}.
z~ = ( z -
tid:
z" Hay rhttnq minA
k= 1
Do d6 , to. chi cAn chung lJiinh z, = y'r(cos;e2 • duong thllng do. Ta eo
~ 11
o Li1i giai. Nt3-U z
Khi d6 t ~p g-iii lrj ella
=,': I .Z2.'··,
=
21 .'::2.2J
= 1 hay
Z2·ZJ
= 1. Do d6 :;·4
www.vnmath.com
Bni 1.14. (:111£119 mtnh rdng. tJdi 91a 11'1 k
tntll!
>
O. k of:. 1. l)luUlng
,
t
_ -.0
L en h~l £~ va n.,
BM 1 .15. ChUng mmh rang ncu cJlUO'
z-b 1 ~I~k
hi plu/d1l9 lrinh littiJng iron. Tim tiim va ban I.;inh duiJng tron (16 . Lui giili. Xct pho'dng lrlllh
I, -al -o-b
(I) "'ang duang vd' Do do
Llji giai. DM arge n = ~k.
(I )
1c..1 '" --Re C n, COSCk ~
0
VI chui)i
(l-k')'
lal' - k'lbI' 1-
k2
en hQi t1,l nen chuoi
L
He en hi;li tv, do d6 chuoi
,,=1
f: 10,.1 hOi W (theo (1», n=1
(2)
Ta 0 ta c6
= R;
y2
C2 _
+ 2i.cg
nen u
=
x
2
-
y"l, V
.
v- O.
tn,le
< 0 ta co
CllH
.
n
. Anh cue dUClng 1.; 1 = Ie. dubn mnh ci18 duong trbll u2 + v 2 = R.4. g
lhAng Y
= ±r.
_y2
1\
= 1;
= ---; u
x2
+ y2
.r-ty
= ~+ x Y
';I'
V{l.y
y = ----, x'l + y2
=C
ta xet hsi l.ntbng hOp: 1 +) N~1l c=O: Tn c6 u=O vo. v=--· Do -00 < y
1 bi~u thallI! C \ \-1: 1}, o
21rJ
Bni 1.41. Cho n dl~ll\ P J = cosH
,.
171")
-,n E N,n ~ J
+tMIl
/I
n 1 tn'n hlllh tron dOli vi. Chung minh dU1~ 116 poP} lu khnR.lIg cach gift8. Po va PJ" Bili 1.42. Cho 0 < r
chubi