{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 "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 "Purple Emphasis" -1 259 "Times" 1 12 102 0 230 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "Red Emphasis" -1 260 "Times " 1 12 255 0 0 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "Dark Red Emphasis" -1 261 "Times" 1 12 128 0 0 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "Grey Emphasis " -1 262 "Times" 1 12 96 52 84 1 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 264 "" 0 1 0 0 0 0 1 0 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 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 }} {SECT 0 {PARA 3 "" 0 "" {TEXT -1 38 "Linear functions of a complex var iable" }}{PARA 0 "" 0 "" {TEXT -1 37 "by Peter Stone, Nanaimo, B.C., C anada" }}{PARA 0 "" 0 "" {TEXT -1 19 "Version: 27.3.2007" }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restar t;" }}}{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 262 9 "complex.m" } {TEXT -1 37 " contains the code for the procedure " }{TEXT 0 13 "confo rmalplot" }{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 11 "Translation" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}}{PARA 0 "" 0 "" {TEXT -1 34 "A function of the form F(z) = z + \+ " }{XPPEDIT 18 0 "alpha;" "6#%&alphaG" }{TEXT -1 8 ", where " } {XPPEDIT 18 0 "alpha;" "6#%&alphaG" }{TEXT -1 139 " is a fixed complex number, corresponds to a translation with horizontal and vertical shi fts determined by the real and imaginary parts of " }{XPPEDIT 18 0 "al pha;" "6#%&alphaG" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 92 "We c an illustrate such a translation by showing what happens to a finite r ectangular region." }}{PARA 0 "" 0 "" {TEXT -1 1 " " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 101 "conformalplot(z,z=-1-I..1+I,color=[green,b rown],\n adaptive=false,thickness=2);" }}{PARA 13 "" 1 "" {GLPLOT2D 180 159 159 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cp7$F^dlFfp7$F^dlFip7$F^dlF\\q7$F^dlF_qFbq-F$6$7A7$$\"+++++5FaqF(7$Fbf lF,7$FbflF07$FbflF37$FbflF67$FbflF97$FbflF<7$FbflF?7$FbflFB7$FbflFE7$F bflFH7$FbflFK7$FbflFN7$FbflFQ7$FbflFT7$FbflFX7$FbflFen7$FbflFhn7$FbflF [o7$FbflF^o7$FbflFao7$FbflFdo7$FbflFgo7$FbflFjo7$FbflF]p7$FbflF`p7$Fbf lFcp7$FbflFfp7$FbflFip7$FbflF\\q7$FbflF_qFbq-F$6$7AF'7$F,F(7$F0F(7$F3F (7$F6F(7$F9F(7$F " 0 "" {MPLTEXT 1 0 125 "alpha := 2+I;\nconformalplot(z+alpha,z=-1-I..1+I,color=[green,bro wn],\n adaptive=false,thickness=2,view=[-1..3,-1..2]);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%&alphaG^$\"\"#\"\"\"" }}{PARA 13 "" 1 "" {GLPLOT2D 283 227 227 {PLOTDATA 2 "6:-%'CURVESG6$7A7$$\"\"\"\"\"! $F*F*7$F($\"*nmmm'!#57$F($\"+MLLL8F/7$F($\"+,+++?F/7$F($\"+ommmEF/7$F( $\"+NLLLLF/7$F($\"+-+++SF/7$F($\"+pmmmYF/7$F($\"+OLLL`F/7$F($\"+.+++gF /7$F($\"+qmmmmF/7$F($\"+PLLLtF/7$F($\"+/+++!)F/7$F($\"+rmmm')F/7$F($\" +QLLL$*F/7$F($\"+++++5!\"*7$F($\"+nmmm5FZ7$F($\"+MLLL6FZ7$F($\"+++++7F 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" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 111 "conformalplot(z,z=-1 -I..1+I,color=[cyan_green,magenta_blue],\n adapti ve=false,thickness=2);" }}{PARA 13 "" 1 "" {GLPLOT2D 180 159 159 {PLOTDATA 2 "69-%'CURVESG6$7A7$$!\"\"\"\"!F(7$F($!+LLLL$*!#57$F($!+mmm m')F.7$F($!+********zF.7$F($!+KLLLtF.7$F($!+lmmmmF.7$F($!+)*******fF.7 $F($!+JLLL`F.7$F($!+kmmmYF.7$F($!+(*******RF.7$F($!+ILLLLF.7$F($!+jmmm EF.7$F($!+'*******>F.7$F($!+HLLL8F.7$F($!+Bmmmm!#67$F($\"#WFV7$F($\"+6 nmmmFV7$F($\"+QLLL8F.7$F($\"+0+++?F.7$F($\"+smmmEF.7$F($\"+RLLLLF.7$F( $\"+1+++SF.7$F($\"+tmmmYF.7$F($\"+SLLL`F.7$F($\"+2+++gF.7$F($\"+ummmmF .7$F($\"+TLLLtF.7$F($\"+3+++!)F.7$F($\"+vmmm')F.7$F($\"+ULLL$*F.7$F($ \"+,+++5!\"*-%&COLORG6&%$RGBG$\"+++++5FaqF*\"\"\"-F$6$7A7$$!+++++!)F.F (7$F]rF,7$F]rF07$F]rF37$F]rF67$F]rF97$F]rF<7$F]rF?7$F]rFB7$F]rFE7$F]rF H7$F]rFK7$F]rFN7$F]rFQ7$F]rFT7$F]rFX7$F]rFen7$F]rFhn7$F]rF[o7$F]rF^o7$ F]rFao7$F]rFdo7$F]rFgo7$F]rFjo7$F]rF]p7$F]rF`p7$F]rFcp7$F]rFfp7$F]rFip 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