{VERSION 6 0 "IBM INTEL NT" "6.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 1 }{CSTYLE "2D Comment" -1 18 "Times" 0 1 0 0 0 0 0 0 2 2 2 
2 0 0 0 1 }{CSTYLE "2D Output" -1 20 "Times" 0 1 0 0 255 1 0 0 2 2 2 
2 0 0 0 1 }{CSTYLE "_cstyle2" -1 205 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 
0 0 0 1 }{CSTYLE "_cstyle3" -1 206 "Times" 1 14 0 0 0 1 2 1 2 2 2 2 0 
0 0 1 }{CSTYLE "_cstyle4" -1 207 "Courier" 1 12 255 0 0 1 2 1 2 2 1 2 
0 0 0 1 }{CSTYLE "" 206 256 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }
{CSTYLE "" 205 257 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 
258 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 
{CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 
0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Ti
mes" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }
{PSTYLE "_pstyle1" -1 201 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 
2 2 2 2 1 1 1 1 }1 1 0 0 0 0 2 0 2 0 2 2 0 1 }{PSTYLE "_pstyle3" -1 
203 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 
0 0 8 2 2 0 2 0 2 2 0 1 }}
{SECT 0 {SECT 1 {PARA 203 "" 0 "" {TEXT 256 10 "Exercice 6" }{TEXT -1 
0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 258 0 "" }{TEXT -1 0 "" }}
{PARA 201 "" 0 "" {TEXT 205 2 "1)" }}{PARA 201 "" 0 "" {TEXT -1 0 "" }
}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 207 41 "restart:z:=(2*sqrt(3)+2
)+I*(2*sqrt(3)-2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"zG,(*$-%%sqr
tG6#\"\"$\"\"\"\"\"#F,F+*&,&F&F,F,!\"\"F+^#F+F+F+" }}}{PARA 201 "" 0 "
" {TEXT -1 0 "" }}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 207 51 "l1:=(m
ap(Re,[seq(simplify(evalc(z^n)),n=1..50)])): " }{TEXT -1 17 "partie r
\351elle de " }{XPPEDIT 18 0 "z^n;" "6#)%\"zG%\"nG" }{TEXT -1 6 " pour
 " }{XPPEDIT 18 0 "n;" "6#%\"nG" }{TEXT -1 17 " allant de 1 \340 50" }
}}{PARA 201 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 201 "> " 0 "" 
{MPLTEXT 1 207 49 "l2:=[seq([n,Re(simplify(evalc(z^n)))],n=1..50)]: " 
}{XPPEDIT 18 0 "n;" "6#%\"nG" }{TEXT -1 21 " et partie r\351elle de " 
}{XPPEDIT 18 0 "z^n;" "6#)%\"zG%\"nG" }{TEXT -1 6 " pour " }{XPPEDIT 
18 0 "n;" "6#%\"nG" }{TEXT -1 17 " allant de 1 \340 50" }}}{PARA 201 "
" 0 "" {TEXT -1 0 "" }}{PARA 201 "" 0 "" {TEXT 205 29 "La boucle suiva
nte extrait de" }{TEXT 257 1 " " }{TEXT 205 13 "l2 les rangs " }
{XPPEDIT 18 0 "n;" "6#%\"nG" }{TEXT 205 35 " pour lesquels la partie r
\351elle de " }{XPPEDIT 18 0 "z^n;" "6#)%\"zG%\"nG" }{TEXT 205 12 " es
t nulle. " }}{PARA 201 "" 0 "" {TEXT 205 1 " " }}{EXCHG {PARA 201 "> \+
" 0 "" {MPLTEXT 1 207 82 "for k from 1 to nops(l2) do  \nif (op(2,op(k
,l2))=0)  then print(k) \nend if\nend do;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#=" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#\"#I" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#U
" }}}{PARA 201 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 14 "Il
 semble que " }{XPPEDIT 18 0 "z^n;" "6#)%\"zG%\"nG" }{TEXT -1 31 " est
 un imaginaire pur lorsque " }{XPPEDIT 18 0 "n;" "6#%\"nG" }{TEXT -1 
27 " est congru \340 6 modulo 12. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 201 "" 0 "" {TEXT 205 3 "2) " }}{PARA 201 "" 0 "" {TEXT -1 0 "" 
}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 207 74 "l:=[seq([n,Re(simplify
(evalc(z^n))),Im(simplify(evalc(z^n)))],n=1..100)]: " }{TEXT -1 57 "le
s \351l\351ments de la liste l sont des triplets mentionnant " }
{XPPEDIT 18 0 "n;" "6#%\"nG" }{TEXT -1 22 ", la partie r\351elle de " 
}{XPPEDIT 18 0 "z^n;" "6#)%\"zG%\"nG" }{TEXT -1 27 "et la partie imagi
naire de " }{XPPEDIT 18 0 "z^n;" "6#)%\"zG%\"nG" }{TEXT -1 2 " ." }}}
{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 207 82 "for k from 1 to nops(l) \+
do\nif (op(2,op(k,l))<=0 and op(3,op(k,l))=0) then print(k)" }{TEXT 
-1 21 " la partie r\351elle de " }{XPPEDIT 18 0 "z^n;" "6#)%\"zG%\"nG
" }{TEXT -1 49 " doit \352tre n\351gative et sa partie imaginaire null
e" }{MPLTEXT 1 207 1 "\n" }{TEXT -1 0 "" }{MPLTEXT 1 207 7 "end if\n" 
}{TEXT -1 0 "" }{MPLTEXT 1 207 7 "end do;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"#7" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#O" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#\"#g" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#%
)" }}}{PARA 201 "" 0 "" {TEXT -1 0 "" }}{PARA 201 "" 0 "" {TEXT -1 14 
"Il semble que " }{XPPEDIT 18 0 "z^n;" "6#)%\"zG%\"nG" }{TEXT -1 30 " \+
soit un r\351el n\351gatif lorsque " }{XPPEDIT 18 0 "n;" "6#%\"nG" }
{TEXT -1 28 " est congru \340 12 modulo 24. " }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 102 "for k from 1 to n
ops(l) do\nif (op(2,op(k,l))<=0 and op(3,op(k,l))=0) then print(simpli
fy(evalc(z^k))) " }{TEXT -1 15 "les valeurs de " }{XPPEDIT 18 0 "z^n;
" "6#)%\"zG%\"nG" }{TEXT -1 9 " lorsque " }{XPPEDIT 18 0 "n-12;" "6#,&
%\"nG\"\"\"\"#7!\"\"" }{TEXT -1 23 " est un multiple de 24." }
{MPLTEXT 1 0 1 "\n" }{TEXT -1 0 "" }{MPLTEXT 1 0 14 "end if\nend do;" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#!+C=ut5" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#!=CU7**[F!Q&GR+%zB\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#!OCmu#QO^\\\\%pfGe5))ffq#pZsU\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#![
oC!4'[L')zNjlet#)\\]]tb#=p\\:Ug?@tb/bk\"" }}}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}{PARA 0 "" 0 "" {TEXT -1 15 "Ainsi, lorsque " }{XPPEDIT 18 0 "n
 = 12+24*k;" "6#/%\"nG,&\"#7\"\"\"*&\"#CF'%\"kGF'F'" }{TEXT -1 2 " (" 
}{XPPEDIT 18 0 "k;" "6#%\"kG" }{TEXT -1 27 " \351tant un entier nature
l), " }{XPPEDIT 18 0 "z^n = -2^30(1+2*k);" "6#/)%\"zG%\"nG,$)\"\"#-\"#
I6#,&\"\"\"F.*&F)F.%\"kGF.F.!\"\"" }{TEXT -1 2 " ." }}}}{MARK "0" 0 }
{VIEWOPTS 1 1 0 3 4 1802 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }