{VERSION 5 0 "IBM INTEL NT" "5.0" } {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 Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {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 "Times" 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 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 8 "Set 12.2" }{MPLTEXT 1 0 0 " " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 4 "Q30:" }{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "evalc(sqrt((3+6*I)/2+sqrt((3 +6*I)^2/4+8-6*I)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#^$\"\"#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "-evalc(sqrt((3+6*I)/2+sqr t((3+6*I)^2/4+8-6*I)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#^$!\"#!\"\" " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "evalc(sqrt((3+6*I)/2-sq rt((3+6*I)^2/4+8-6*I)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#^$\"\"\"F$ " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "-evalc(sqrt((3+6*I)/2-s qrt((3+6*I)^2/4+8-6*I)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#^$!\"\"F$ " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 8 "Set 12.3" }{MPLTEXT 1 0 0 "" } }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 4 "Q20:" }{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "eval(diff((3*z^2+I*z)^2,z),z =1+I);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#^$!$5\"\"#q" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 8 "Set 12.4" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "Q8:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "f:=1/(1-(x+y*I)^4): u:=simplify(evalc(Re(f) )); v:=simplify(evalc(Im(f)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\" uG,$*&,*\"\"\"!\"\"*$)%\"xG\"\"%F(F(*(\"\"'F()F,\"\"#F()%\"yGF1F(F)*$) F3F-F(F(F(,4F(F(*&F1F(F+F(F)*(\"#7F(F0F(F2F(F(*&F1F(F5F(F)*$)F,\"\")F( F(*(F-F()F,F/F(F2F(F(*(F/F(F+F(F5F(F(*(F-F(F0F()F3F/F(F(*$)F3F=F(F(F)F )" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"vG,$*,\"\"%\"\"\"%\"xGF(%\"yG F(,&*$)F)\"\"#F(F(*$)F*F.F(!\"\"F(,4F(F(*&F.F()F)F'F(F1*(\"#7F(F-F(F0F (F(*&F.F()F*F'F(F1*$)F)\"\")F(F(*(F'F()F)\"\"'F(F0F(F(*(F>F(F4F(F8F(F( *(F'F(F-F()F*F>F(F(*$)F*F;F(F(F1F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "simplify(diff(u,x)-diff(v,y));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "sim plify(diff(u,y)+diff(v,x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 4 "Q12:" }{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "f:=Re((x+I*y)^2)-I*Im((x+I*y )^2): u:=evalc(Re(f)); v:=evalc(Im(f));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"uG,&*$)%\"xG\"\"#\"\"\"F**$)%\"yGF)F*!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"vG,$*(\"\"#\"\"\"%\"xGF(%\"yGF(!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "simplify(diff(u,x)-diff(v,y)); # \+ not analytic" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&\"\"%\"\"\"%\"xGF& F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "simplify(diff(u,y)+di ff(v,x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&\"\"%\"\"\"%\"yGF&!\" \"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 4 "Q24:" }{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "u:=(x^2-y^2)^2: diff(u,x,x) +diff(u,y,y); # not harmonic" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*& \"\")\"\"\")%\"xG\"\"#F&F&*&F%F&)%\"yGF)F&F&" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 8 "Set 12.6" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 4 "Q14:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "x:=ln(abs(4+3*I));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%\"xG-%#lnG6#\"\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "y:= argument(4+3*I)+[seq(2*Pi*i,i=-4..4)];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"yG,&-%'arctanG6##\"\"$\"\"%\"\"\"7+,$*&\"\")F,%#PiGF,!\"\",$ *&\"\"'F,F1F,F2,$*&F+F,F1F,F2,$*&\"\"#F,F1F,F2\"\"!,$*&F:F,F1F,F,,$*&F +F,F1F,F,,$*&F5F,F1F,F,,$*&F0F,F1F,F,F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "evalf(evalm(%));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#- %'vectorG6#7+$!+7S#*[C!\")$!+\"[01#=F)$!+^pG#>\"F)$!+*>%oRc!\"*$\"+)36 ]V'!#5$\"+F)$\"+MUixDF)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 8 "Set 12.8" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "Q6" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 20 "evalc(ln(-12-16*I));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&-%#lnG6#\"#?\"\"\"*&,&-%'arctanG6##\"\"%\"\"$F(%#PiG! \"\"F(^#F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#^$$\"+uAt&*H!\"*$!+OuH9AF&" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "Q22" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "evalc(ln(1+I));" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#,&*&#\"\"\"\"\"#F&-%#lnG6#F'F&F&*&^##F&\"\"%F&%#PiGF& F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "evalc((1-I)*%);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,(*&#\"\"\"\"\"#F&-%#lnG6#F'F&F&*&\"\" %!\"\"%#PiGF&F&*&,&*&#F&F'F&F(F&F-*&F,F-F.F&F&F&^#F&F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "evalc(exp(%));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&-%$expG6#,&*&#\"\"\"\"\"#F+-%#lnG6#F,F+F+*&\"\"%!\" \"%#PiGF+F+F+-%$cosG6#,&*&#F+F,F+F-F+F2*&F1F2F3F+F+F+F+*(F%F+-%$sinGF6 F+^#F+F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#^$$\"+)Hzy!G!\"*$\"+u^'yJ\"F&" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 18 "or, more directly:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "evalc((1+I)^(1.-I)); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#^$$\"+(Hzy!G!\"*$\"+t^'yJ\"F&" }}} }{MARK "36" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }