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{SECT 0 {SECT 1 {PARA 203 "" 0 "" {TEXT 256 10 "Exercice 4" }{TEXT -1 
0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 201 "" 0 "" {TEXT 205 60 
"V\351rifions le r\351sultat annonc\351 pour un complexe particulier. \+
" }}{PARA 201 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 201 "> " 0 "" 
{MPLTEXT 1 207 8 "restart;" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 
207 17 "z:=polar(1,Pi/4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"zG-%&
polarG6$\"\"\",$%#PiG#F(\"\"%" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 
1 207 15 "Z:=(1-z)/(1+z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"ZG*&,
&\"\"\"F'-%&polarG6$F',$%#PiG#F'\"\"%!\"\"F',&F'F'F(F'F/" }}}{EXCHG 
{PARA 201 "> " 0 "" {MPLTEXT 1 207 21 "simplify(evalc((Z)));" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#*&*&^#!\"\"\"\"\"-%%sqrtG6#\"\"#F'F',&F+F'*$
F(F'F'F&" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 207 30 "simplify(ev
alc(conjugate(Z)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&*&-%%sqrtG6#
\"\"#\"\"\"^#F)F)F),&F(F)*$F%F)F)!\"\"" }}}{PARA 201 "" 0 "" {TEXT 
205 1 " " }}{PARA 201 "" 0 "" {TEXT 205 67 "Comme Z et son conjugu\351
 son oppos\351s, Z est bien un imaginaire pur. " }}{PARA 201 "" 0 "" 
{TEXT -1 0 "" }}{PARA 201 "" 0 "" {TEXT 205 51 "V\351rifions le r\351s
ultat annonc\351 dans le cas g\351n\351ral. " }}{PARA 201 "" 0 "" 
{TEXT -1 0 "" }}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 207 20 "assume(t
heta,real): " }{XPPEDIT 18 0 "theta;" "6#%&thetaG" }{TEXT -1 23 " est \+
un r\351el quelconque" }{MPLTEXT 1 207 3 "   " }{TEXT -1 2 "  " }
{MPLTEXT 1 207 3 "   " }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 201 "> " 0 "
" {MPLTEXT 1 207 19 "z:=polar(1,theta); " }{TEXT -1 47 "z est le compl
exe de module 1, d'argument theta" }{MPLTEXT 1 207 1 " " }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%\"zG-%&polarG6$\"\"\"%'theta|irG" }}}{EXCHG 
{PARA 201 "> " 0 "" {MPLTEXT 1 207 15 "asssume(z<>-1);" }{TEXT -1 28 "
 on suppose z diff\351rent de 1" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%(
asssumeG6#0-%&polarG6$\"\"\"%'theta|irG!\"\"" }}}{EXCHG {PARA 201 "> \+
" 0 "" {MPLTEXT 1 207 16 "Z:=(1-z)/(1+z); " }{TEXT -1 12 "on d\351fini
t Z" }{MPLTEXT 1 207 1 " " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"ZG*&,
&\"\"\"F'-%&polarG6$F'%'theta|irG!\"\"F',&F'F'F(F'F," }}}{PARA 201 "" 
0 "" {TEXT -1 0 "" }}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 207 59 "eva
lb((simplify(evalc(conjugate(Z))))=-simplify(evalc(Z)));" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#%%trueG" }}}{PARA 201 "" 0 "" {TEXT -1 0 "" }}
{PARA 201 "" 0 "" {TEXT 205 88 "Cette ligne montre que Z et son conjug
u\351 sont oppos\351s, et que Z est un imaginaire pur.  " }}{PARA 201 
"" 0 "" {TEXT -1 0 "" }}{PARA 201 "" 0 "" {TEXT 205 61 "Attention. La \+
commande pr\351c\351dente priv\351e de 'simplify' donne " }{TEXT 257 
5 "false" }{TEXT 205 137 " : pour Maple, deux complexes \351crits sous
 forme alg\351brique pour l'un et sous forme exponentielle pour l'autr
e, sont forc\351ment diff\351rents." }{TEXT -1 0 "" }}}{PARA 0 "" 0 "
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