{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 Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 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 } {CSTYLE "" -1 23 "Courier" 1 10 0 0 0 0 0 0 0 0 0 0 3 0 0 1 }{CSTYLE " Blue Emphasis" -1 256 "Times" 0 0 0 0 255 1 0 1 0 0 0 0 0 0 0 1 } {CSTYLE "Green Emphasis" -1 257 "Times" 1 12 0 128 0 1 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "Maroon Emphasis" -1 258 "Times" 1 12 128 0 128 1 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 261 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 262 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "Purple Emphasis" -1 263 "Times" 1 12 102 0 230 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "Red Emphasis" -1 264 "Tim es" 1 12 255 0 0 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "Dark Red Emphasis" -1 265 "Times" 1 12 128 0 0 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 266 " " 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 267 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 268 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "Grey Emphasis" -1 269 "Times" 1 12 96 52 84 1 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 "Heading 1 " -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 128 1 2 1 2 2 2 2 1 1 1 1 } 1 1 0 0 8 4 3 0 3 0 2 2 0 1 }{PSTYLE "Heading 2" -1 4 1 {CSTYLE "" -1 -1 "Times" 1 14 128 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 2 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 }{PSTYLE "Maple Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 256 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {PARA 3 "" 0 "" {TEXT -1 39 "Plotting complex solutions of equ ations" }}{PARA 0 "" 0 "" {TEXT -1 37 "by Peter Stone, Nanaimo, B.C., \+ Canada" }}{PARA 0 "" 0 "" {TEXT -1 19 "Version: 26.3.2007" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "resta rt;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 35 "load procedures for complex numbers" }}{PARA 0 "" 0 "" {TEXT -1 17 "The Maple m-file " }{TEXT 269 9 "complex.m" } {TEXT -1 37 " contains the code for the procedure " }{TEXT 0 11 "plotc omplex" }{TEXT -1 25 " used in this worksheet. " }}{PARA 0 "" 0 "" {TEXT -1 123 "It can be read into a Maple session by a command similar to the one that follows, where the file path gives its location. " } }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "read \"K:\\\\Maple/procdrs/ complex.m\";" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}{SECT 1 {PARA 4 "" 0 " " {TEXT -1 39 "Plotting complex solutions of equations" }}{PARA 0 "" 0 "" {TEXT -1 26 "We can solve the equation " }{XPPEDIT 18 0 "z^3-1 = \+ 0;" "6#/,&*$%\"zG\"\"$\"\"\"F(!\"\"\"\"!" }{TEXT -1 18 " by using Mapl e's " }{TEXT 0 5 "solve" }{TEXT -1 9 " command." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "soln := [fso lve(z^8+3*z^2-1=0,z,complex)];" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%%s olnG7*,&$!+86K-5!\"*\"\"\"%\"IG$!+?)e4K'!#5,&F'F*F+$\"+?)e4K'F.$!+OATR dF.,$F+$!+o:\"3C\"F),$F+$\"+o:\"3C\"F)$\"+OATRdF.,&$\"+86K-5F)F*F+F,,& F=F*F+F0" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 23 "Given a complex number " }{XPPEDIT 18 0 "z = x + y*i" "6#/%\"zG,&% \"xG\"\"\"*&%\"yGF'%\"iGF'F'" }{TEXT -1 16 " with real part " }{TEXT 266 1 "x" }{TEXT -1 20 " and imaginary part " }{TEXT 267 1 "y" }{TEXT -1 25 ", the following function " }{TEXT 0 4 "vect" }{TEXT -1 55 " can be used to obtain the position vector of the point" }{XPPEDIT 18 0 "` `(x,y)" "6#-%!G6$%\"xG%\"yG" }{TEXT -1 43 " in a 2-dimensional plane w hich represents " }{TEXT 268 1 "z" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 76 "This function can be applied to a list of solutions via t he Maple procedure " }{TEXT 0 3 "map" }{TEXT -1 52 " to obtain a corre sponding list of position vectors." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "vect := z -> [[0,0],[Re(z),I m(z)]];\nvectors := map(vect,soln);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%%vectGf*6#%\"zG6\"6$%)operatorG%&arrowGF(7$7$\"\"!F.7$-%#ReG6#9$-%# ImGF2F(F(F(" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%(vectorsG7*7$7$\"\"!F (7$$!+86K-5!\"*$!+?)e4K'!#57$F'7$F*$\"+?)e4K'F/7$F'7$$!+OATRdF/F(7$F'7 $F($!+o:\"3C\"F,7$F'7$F($\"+o:\"3C\"F,7$F'7$$\"+OATRdF/F(7$F'7$$\"+86K -5F,F-7$F'7$FFF2" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "plot(vectors,color=brown,thickness=2,scaling= constrained);" }}{PARA 13 "" 1 "" {GLPLOT2D 272 274 274 {PLOTDATA 2 "6 /-%'CURVESG6#7$7$\"\"!F(7$$!1+++86K-5!#:$!1+++?)e4K'!#;-F$6#7$F'7$F*$ \"1+++?)e4K'F/-F$6#7$F'7$$!1+++OATRdF/F(-F$6#7$F'7$F($!1+++o:\"3C\"F,- F$6#7$F'7$F($\"1+++o:\"3C\"F,-F$6#7$F'7$$\"1+++OATRdF/F(-F$6#7$F'7$$\" 1+++86K-5F,F--F$6#7$F'7$FRF4-%+AXESLABELSG6$%!GFen-%(SCALINGG6#%,CONST RAINEDG-%*THICKNESSG6#\"\"#-%'COLOURG6&%$RGBG$\")#)eqk!\")$\"))eqk\"Fd oFeo-%%VIEWG6$%(DEFAULTGFjo" 1 2 0 1 10 2 2 6 1 4 1 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 14 "The procedure " }{TEXT 0 11 "plotcomplex " }{TEXT -1 47 " given in the next section can do a better job." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 49 "A procedure for plottin g a list complex numbers: " }{TEXT 0 11 "plotcomplex" }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}} {SECT 1 {PARA 4 "" 0 "" {TEXT -1 18 "plotcomplex: usage" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 259 18 "Call ing Sequence:\n" }}{PARA 0 "" 0 "" {TEXT 260 2 " " }{TEXT -1 21 " p lotcomplex( zz ) " }{TEXT 261 1 "\n" }{TEXT -1 0 "" }}{PARA 256 "" 0 " " {TEXT -1 11 "Parameters:" }}{PARA 0 "" 0 "" {TEXT -1 5 " " }} {PARA 0 "" 0 "" {TEXT 23 10 " zz - " }{TEXT -1 30 " a list of com plex constants." }}{PARA 0 "" 0 "" {TEXT -1 6 " " }}{PARA 256 "" 0 "" {TEXT -1 12 "Description:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 14 "The procedure " }{TEXT 0 11 "plotcomplex " }{TEXT -1 67 " plots the position vectors of the complex numbers in \+ a given list." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 262 8 "Options:" }{TEXT -1 1 "\n" }}{PARA 0 "" 0 "" {TEXT -1 20 "style=vectors/points" }}{PARA 0 "" 0 "" {TEXT -1 83 "This option allo ws the points alone to be plotted instead of the position vectors. " } }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 78 "colour=c or color =c,\nwhere c is \"hue\", a single colour, or a list of colou rs." }}{PARA 0 "" 0 "" {TEXT -1 143 "In the case color=\"hue\" the co lour is determined by the argument of the complex number z in the list zz. More precisely, the hue is given by " }{XPPEDIT 18 0 "1/2+arg(z) /(2*Pi);" "6#,&*&\"\"\"F%\"\"#!\"\"F%*&-%$argG6#%\"zGF%*&F&F%%#PiGF%F' F%" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 45 "The alternative for m color=\"HUE\" may be used." }}{PARA 0 "" 0 "" {TEXT -1 265 "When a l ist of colours is supplied, the colours in the list are used to colour the position vectors corresponding to the complex numbers in the list zz in the order given. If there are more complex position vectors tha n colours, the colours are repeated cyclically." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 12 "thickness=n " }}{PARA 0 " " 0 "" {TEXT -1 165 "n can be a single positive integer or a list of p ositive integers to specify the thicknesses of the lines drawn to repr esent the complex numbers as position vectors." }}{PARA 0 "" 0 "" {TEXT -1 308 "When a list of positive integers is supplied, the number s in the list are used to specify the thicknesses of the lines for the position vectors corresponding to the complex numbers in the list zz \+ in the order given. If there are more complex numbers than thicknesses , the thicknesses are repeated cyclically." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 12 "linestyle=n " }}{PARA 0 "" 0 " " {TEXT -1 164 "n can be a single positive integer or a list of positi ve integers to specify the linestyles of the lines drawn to represent \+ the complex numbers as position vectors." }}{PARA 0 "" 0 "" {TEXT -1 305 "When a list of positive integers is supplied, the numbers in the \+ list are used to specify the linestyles of the lines for the position \+ vectors corresponding to the complex numbers in the list zz in the ord er given. If there are more complex numbers than linestyles, the lines tyles are repeated cyclically." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 263 16 "How to a ctivate:" }{TEXT 256 1 "\n" }{TEXT -1 154 "To make the procedure activ e open the subsection, place the cursor anywhere after the prompt [ > \+ and press [Enter].\nYou can then close up the subsection." }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 27 "plotcomplex: implementation" }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "stdeuler" {MPLTEXT 1 0 2821 "plotcomplex := proc(zz::list(complexcons))\n local Options,sty l,thck,lnstyl,tt,clr,z,pp,hh,n,m,i,c,t;\n\n # Get the options.\n # Set the default values to start with.\n hh := true:\n thck := [2] ;\n lnstyl := [1];\n styl := 'vectors';\n if nargs>1 then\n \+ Options:=[args[2..nargs]];\n if not type(Options,list(equation)) then\n error \"each optional argument must be an equation\"\n end if;\n if hasoption(Options,'color','tt','Options') \n \+ or hasoption(Options,'colour','tt','Options') then\n if tt='HUE' or tt='hue' then hh := true\n else\n hh : = false; \n if not type(tt,list) then tt := [tt] end if;\n \+ clr := [];\n for i to nops(tt) do\n \+ clr := [op(clr),`plot/color`(tt[i])];\n end do;\n \+ end if;\n end if;\n if hasoption(Options,'thickness','thck' ,'Options') then\n if type(thck,posint) then thck := [thck] en d if;\n if not type(thck,list(posint)) then\n error \"\\\"thickness\\\" must be a positive integer or a list of positive \+ integers\"\n end if;\n end if;\n if hasoption(Option s,'linestyle','lnstyl','Options') then\n if type(lnstyl,posint ) then lnstyl := [lnstyl] end if;\n if not type(lnstyl,list(po sint)) then\n error \"\\\"linestyle\\\" must be a positive \+ integer or a list of positive integers\"\n end if;\n end \+ if;\n if hasoption(Options,'style','styl','Options') then\n \+ print(Options);\n if not member(styl,\{points,vectors\}) th en\n error \"\\\"style\\\" must be either 'points' or 'vect ors'\"\n end if;\n end if;\n if nops(Options)>0 then \n error \"%1 is not a valid option for %2\",op(1,Options),pro cname;\n end if;\n end if;\n\n n := nops(zz);\n if hh then \+ \n clr := [seq(COLOR(HUE,evalf(0.5+argument(zz[i])/(2*Pi))),i=1.. n)];\n else\n m := nops(clr);\n clr := [seq(clr[`mod`(i,m) +1],i=0..n-1)];\n end if;\n if styl='vectors' then\n m := nop s(thck);\n thck := [seq(thck[`mod`(i,m)+1],i=0..n-1)];\n m : = nops(lnstyl);\n lnstyl := [seq(lnstyl[`mod`(i,m)+1],i=0..n-1)]; \n PLOT(seq(CURVES([[0,0],[Re(zz[i]),Im(zz[i])]],\n THICK NESS(thck[i]),LINESTYLE(lnstyl[i]),clr[i]),i=1..n),\n seq(POIN TS([Re(zz[i]),Im(zz[i])],SYMBOL(CIRCLE),clr[i]),i=1..n),\n seq (POINTS([Re(zz[i]),Im(zz[i])],SYMBOL(DIAMOND),clr[i]),i=1..n),\n \+ seq(POINTS([Re(zz[i]),Im(zz[i])],SYMBOL(CROSS),clr[i]),i=1..n), \+ \n SCALING(CONSTRAINED));\n else\n PLOT(seq(POINTS([R e(zz[i]),Im(zz[i])],SYMBOL(CIRCLE),clr[i]),i=1..n),\n seq(POIN TS([Re(zz[i]),Im(zz[i])],SYMBOL(DIAMOND),clr[i]),i=1..n),\n se q(POINTS([Re(zz[i]),Im(zz[i])],SYMBOL(CROSS),clr[i]),i=1..n), \n \+ SCALING(CONSTRAINED));\n end if;\nend proc: " }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{SECT 1 {PARA 4 "" 0 " " {TEXT 0 11 "plotcomplex" }{TEXT -1 10 ": examples" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 10 "E xample 1 " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "u := 4+3*I;\nplotcomplex([u,conjugate(u),-u,-conjugat e(u)]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"uG^$\"\"%\"\"$" }} {PARA 13 "" 1 "" {GLPLOT2D 283 222 222 {PLOTDATA 2 "63-%'CURVESG6&7$7$ \"\"!F(7$\"\"%\"\"$-%*THICKNESSG6#\"\"#-%*LINESTYLEG6#\"\"\"-%&COLORG6 $%$HUEG$\"+CQ;Cg!#5-F$6&7$F'7$F*!\"$F,F0-F56$F7$\"+wh$e(RF:-F$6&7$F'7$ !\"%F?F,F0-F56$F7$\"+CQ;C5F:-F$6&7$F'7$FHF+F,F0-F56$F7$\"+wh$e(*)F:-%' POINTSG6%F)-%'SYMBOLG6#%'CIRCLEGF4-FV6%F>FXF@-FV6%FGFXFI-FV6%FPFXFQ-FV 6%F)-FY6#%(DIAMONDGF4-FV6%F>F^oF@-FV6%FGF^oFI-FV6%FPF^oFQ-FV6%F)-FY6#% &CROSSGF4-FV6%F>FioF@-FV6%FGFioFI-FV6%FPFioFQ-%(SCALINGG6#%,CONSTRAINE DG" 1 2 0 1 10 0 2 9 1 4 1 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10" "Curve 11" "Curve 12" "Curve 13" "Curve 14" "Curv e 15" "Curve 16" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 9 "Exa mple 2" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "u := 5 + 12*I;\ns := sqrt(u);\nplotcomplex([u,s,-s]); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"uG^$\"\"&\"#7" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG^$\"\"$\"\"#" }}{PARA 13 "" 1 "" {GLPLOT2D 360 270 270 {PLOTDATA 2 "60-%'CURVESG6$7$7$\"\"!F(7$!\"$!\"#-%&COLORG6 $%$HUEG$\"*5_$e$*!#5-F$6$7$F'7$\"\"$\"\"#-F-6$F/$\"+4_$e$fF2-F$6$7$F'7 $\"\"&\"#7-F-6$F/$\"+=/nroF2-%'POINTSG6%F6-%'SYMBOLG6#%'CIRCLEGF9-FH6% F6-FK6#%(DIAMONDGF9-FH6%F6-FK6#%&CROSSGF9-FH6%F@FJFC-FH6%F@FPFC-FH6%F@ FUFC-FH6%F)FJF,-FH6%F)FPF,-FH6%F)FUF,-%*THICKNESSG6#F8-%(SCALINGG6#%,C ONSTRAINEDG" 1 2 0 1 10 2 2 9 1 4 1 1.000000 45.000000 45.000000 0 0 " Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7" " Curve 8" "Curve 9" "Curve 10" "Curve 11" "Curve 12" }}}}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}} {SECT 1 {PARA 4 "" 0 "" {TEXT -1 10 "Example 3 " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 88 "soln := fsol ve(z^3=1,z,complex);\nplotcomplex([soln],color=[red,green,blue],thickn ess=3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%solnG6%^$$!+++++]!#5$!+Q SDg')F)^$F'$\"+QSDg')F)$\"\"\"\"\"!" }}{PARA 13 "" 1 "" {GLPLOT2D 360 270 270 {PLOTDATA 2 "6/-%'CURVESG6&7$7$\"\"!F(7$$!+++++]!#5$!+QSDg')F, -%*THICKNESSG6#\"\"$-%*LINESTYLEG6#\"\"\"-%'COLOURG6&%$RGBG$\"*++++\"! \")$F(F(F>-F$6&7$F'7$F*$\"+QSDg')F,F/F3-F86&F:F>F;F>-F$6&7$F'7$$F6F(F> F/F3-F86&F:F>F>F;-%'POINTSG6%F)-%'SYMBOLG6#%'CIRCLEGF7-FO6%FBFQFE-FO6% FJFQFL-FO6%F)-FR6#%(DIAMONDGF7-FO6%FBFenFE-FO6%FJFenFL-FO6%F)-FR6#%&CR OSSGF7-FO6%FBF^oFE-FO6%FJF^oFL-%(SCALINGG6#%,CONSTRAINEDG" 1 2 0 1 10 0 2 9 1 4 1 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curv e 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "Curv e 10" "Curve 11" "Curve 12" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{SECT 1 {PARA 4 "" 0 " " {TEXT -1 10 "Example 4 " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "soln := fsolve(z^8+10=0,z,complex); \nplotcomplex([soln]);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%%solnG6*^$ $!+dJ,K7!\"*$!+)elJ5&!#5^$F'$\"+)elJ5&F,^$F*F'^$F*$\"+dJ,K7F)^$F.F'^$F .F2^$F2F*^$F2F." }}{PARA 13 "" 1 "" {GLPLOT2D 360 270 270 {PLOTDATA 2 "6C-%'CURVESG6&7$7$\"\"!F(7$$!+dJ,K7!\"*$!+)elJ5&!#5-%*THICKNESSG6#\" \"#-%*LINESTYLEG6#\"\"\"-%&COLORG6$%$HUEG$\"*,++D'F/-F$6&7$F'7$F*$\"+) elJ5&F/F0F4-F96$F;$\"+*****\\P*F/-F$6&7$F'7$F-F*F0F4-F96$F;$\"++++v=F/ -F$6&7$F'7$F-$\"+dJ,K7F,F0F4-F96$F;$\"++++D\")F/-F$6&7$F'7$FBF*F0F4-F9 6$F;$\"+,++DJF/-F$6&7$F'7$FBFTF0F4-F96$F;$\"+*****\\(oF/-F$6&7$F'7$FTF -F0F4-F96$F;$\"++++vVF/-F$6&7$F'7$FTFBF0F4-F96$F;$\"++++DcF/-%'POINTSG 6%F)-%'SYMBOLG6#%'CIRCLEGF8-Fep6%FAFgpFD-Fep6%FKFgpFL-Fep6%FSFgpFV-Fep 6%FgnFgpFhn-Fep6%F_oFgpF`o-Fep6%FgoFgpFho-Fep6%F_pFgpF`p-Fep6%F)-Fhp6# %(DIAMONDGF8-Fep6%FAF[rFD-Fep6%FKF[rFL-Fep6%FSF[rFV-Fep6%FgnF[rFhn-Fep 6%F_oF[rF`o-Fep6%FgoF[rFho-Fep6%F_pF[rF`p-Fep6%F)-Fhp6#%&CROSSGF8-Fep6 %FAF^sFD-Fep6%FKF^sFL-Fep6%FSF^sFV-Fep6%FgnF^sFhn-Fep6%F_oF^sF`o-Fep6% FgoF^sFho-Fep6%F_pF^sF`p-%(SCALINGG6#%,CONSTRAINEDG" 1 2 0 1 10 0 2 9 1 4 1 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" " Curve 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10" "Curve 11" "Curve 12" "Curve 13" "Curve 14" "Curve 15" "Curve 16" "Cur ve 17" "Curve 18" "Curve 19" "Curve 20" "Curve 21" "Curve 22" "Curve 2 3" "Curve 24" "Curve 25" "Curve 26" "Curve 27" "Curve 28" "Curve 29" " Curve 30" "Curve 31" "Curve 32" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{SECT 1 {PARA 4 "" 0 " " {TEXT -1 10 "Example 5 " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "soln := [fsolve(z^8-3*z^7+z+10=0,z, complex)];\nplotcomplex(soln);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%%s olnG7*^$$!+Vy,@5!\"*$!+)o/Ai%!#5^$F'$\"+)o/Ai%F,^$$!+\"*G1sKF,$!+)H'z4 6F)^$F1$\"+)H'z46F)^$$\"+*)3\"3&pF,$!+I!*3:5F)^$F9$\"+I!*3:5F)$\"+e " 0 "" {MPLTEXT 1 0 100 "plotcomplex(soln,color=[cyan,blue,magenta,brown,coral,\n y ellow,red,green],thickness=[2$7,3]);" }}{PARA 13 "" 1 "" {GLPLOT2D 476 476 476 {PLOTDATA 2 "6C-%'CURVESG6&7$7$\"\"!F(7$$!+Vy,@5!\"*$!+)o/ Ai%!#5-%*THICKNESSG6#\"\"#-%*LINESTYLEG6#\"\"\"-%'COLOURG6&%$RGBG$F(F( $\"*++++\"!\")F=-F$6&7$F'7$F*$\"+)o/Ai%F/F0F4-F96&F;F " 0 "" {MPLTEXT 1 0 87 "pl otcomplex(soln,style=points,\n color=[cyan,blue,magenta,brown,coral, tan,red,green]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7\"" }}{PARA 13 " " 1 "" {GLPLOT2D 476 476 476 {PLOTDATA 2 "6;-%'POINTSG6%7$$!+Vy,@5!\"* $!+)o/Ai%!#5-%'SYMBOLG6#%'CIRCLEG-%'COLOURG6&%$RGBG$\"\"!F6$\"*++++\"! \")F7-F$6%7$F'$\"+)o/Ai%F,F--F26&F4F5F5F7-F$6%7$$!+\"*G1sKF,$!+)H'z46F )F--F26&F4F7F5F7-F$6%7$FD$\"+)H'z46F)F--F26&F4$\")#)eqkF9$\"))eqk\"F9F S-F$6%7$$\"+*)3\"3&pF,$!+I!*3:5F)F--F26&F4F7$\")AR!)\\F9F5-F$6%7$FX$\" +I!*3:5F)F--F26&F4$\")`B)e)F9$\")fqkdF9$\")p:#R%F9-F$6%7$$\"+e " 0 "" {MPLTEXT 1 0 1 ";" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 19 "Complex Number Song" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 919 "Mine eyes have seen the \+ glory of the Argand Diagram.\nThey have seen the i's and thetas of De \+ Moivre's mighty plan.\003\nNow I can find the complex roots with consu mmate elan.\nWith the root of minus one.\n\nComplex roots are so easy. \nComplex roots are so easy.\nComplex roots are so easy.\nWith the roo t of minus one.\n\nIn Cartesian coordinates the complex plane is fine, \nbut the grandeur of the polar form, this beauty does outshine.\nYou \+ be raising i plus 40 to the power of 99.\nWith the root of minus one. \n\nComplex roots are so easy.\nComplex roots are so easy.\nComplex ro ots are so easy.\nWith the root of minus one.\n\nYou'll realize your u nderstanding was just second rate,\nWhen you see the power and magic o f the complex conjugate,\nDrawing vectors corresponding to the root of minus eight.\nWith the root of minus one.\n\nComplex roots are so eas y.\nComplex roots are so easy.\nComplex roots are so easy.\nWith the r oot of minus one." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 15 " Anon." }}}}{MARK "4 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }