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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT 256 40 "COMPLEX NUMBERS AND VAR
IABLES WITH MAPLE" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 211 "This is the first of a series of  worksheets which illus
trate by example how one can apply the concepts  in  PHYS 312, using t
he software package Maple. It is a good idea to start a new problem wi
th the command " }{TEXT 257 7 "restart" }{TEXT -1 64 " which clears al
l previous definitions and variable assignments!" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
132 "Expressions in Maple are terminated by semicolon \";\" or colon \+
\":\". In the latter case output is suppressed. The imaginary number  \+
i=" }{XPPEDIT 18 0 "sqrt(-1) " "6#-%%sqrtG6#,$\"\"\"!\"\"" }{TEXT -1 
61 " is written as I in Maple. A complex number can be written as" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "a:=5+7*I;" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%\"aG^$\"\"&\"\"(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 17 "Note the use of \"" }{TEXT 258 3 ":= " }{TEXT -1 15 "\" rather \+
than \"" }{TEXT 259 1 "=" }{TEXT -1 405 "\" to assign to the symbol \"
a\"  the value \"5+7I\". Forgetting the colon is one of the most commo
n errors to new users of Maple, particularly if you are used to Mathem
atica. Since no error message results if you use \"=\" instead of \":=
\" this is an error that sometimes can be hard to debug. The equality \+
sign \"=\" in Maple indicates a logical operation: a=b is a statement \+
that can be either \"true\" or \"false\"." }}{PARA 0 "" 0 "" {TEXT -1 
64 "To get a numerical, floating point, value  use the command evalf" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(a);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#^$$\"\"&\"\"!$\"\"(F&" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 42 "The command evalc evaluates the number on " }{XPPEDIT 18 
0 "x+I*y" "6#,&%\"xG\"\"\"*&%\"IGF%%\"yGF%F%" }{TEXT -1 5 " form" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "evalc(a/(1-I));" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#^$!\"\"\"\"'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 79 "Complex numbers can be added, subtracted, multiplied and divide
d the usual way:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "c:=6+3*I
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"cG^$\"\"'\"\"$" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "a+c;" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#^$\"#6\"#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "a-c;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#^$!\"\"\"\"%" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 4 "a*c;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#^$\"\"*\"
#d" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "a/c;" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#^$#\"#<\"#:#\"\"$\"\"&" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 40 "The real and imaginary part is called by" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "Re(a);Im(a);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"(" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 30 "The magnitude is evaluated by " }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "abs(a);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#*$-%%sqrtG6#\"#u\"\"\"" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 37 "while the phase angle (in radians) is" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 31 "argument(a);evalf(argument(a));" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#-%'arctanG6##\"\"(\"\"&" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#$\"+3%oa]*!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 48 "W
hen evaluated, argument gives a number between " }{XPPEDIT 18 0 "-Pi" 
"6#,$%#PiG!\"\"" }{TEXT -1 5 " and " }{XPPEDIT 18 0 "Pi" "6#%#PiG" }
{TEXT -1 2 " ." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "argument(
1-I);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$%#PiG#!\"\"\"\"%" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 4 "not " }{XPPEDIT 18 0 "7*Pi/4;" "6#*
(\"\"(\"\"\"%#PiGF%\"\"%!\"\"" }{TEXT -1 12 " ! Similarly" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "argument(polar(1,1.5*Pi));" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,$%#PiG#!\"\"\"\"#" }}}{EXCHG {PARA 0 
"" 0 "" {TEXT -1 69 "Elementary functions can be called by complex arg
uments and evaluated" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "eva
lf(exp(a));evalf(sin(a));evalf(cos(a));" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#^$$\"+_,*)=6!\"($\"+gca](*!\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#^$$!+_^%zD&!\"($\"+*\\l`b\"F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#^$$
\"+&3o`b\"!\"($\"+3k$zD&F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 42 "We \+
can also use evalc on complex functions" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 42 "evalc(exp(a));evalc(sin(a));evalc(cos(a));" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#,&*&-%$expG6#\"\"&\"\"\"-%$cosG6#\"\"(F)F)*(
^#F)F)F%F)-%$sinGF,F)F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&-%$sinG
6#\"\"&\"\"\"-%%coshG6#\"\"(F)F)*(^#F)F)-%$cosGF'F)-%%sinhGF,F)F)" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&-%$cosG6#\"\"&\"\"\"-%%coshG6#\"\"
(F)F)*(^#!\"\"F)-%$sinGF'F)-%%sinhGF,F)F)" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 67 "When evalc gets unspecified variables Maple assumes them \+
to be real" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "evalc(exp(x+I
*y));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&-%$expG6#%\"xG\"\"\"-%$co
sG6#%\"yGF)F)*(^#F)F)F%F)-%$sinGF,F)F)" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 18 "evalc(sin(x+I*y));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#,&*&-%$sinG6#%\"xG\"\"\"-%%coshG6#%\"yGF)F)*(^#F)F)-%$cosGF'F)-%%sinh
GF,F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "evalc(cos(x+I*y)
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&-%$cosG6#%\"xG\"\"\"-%%coshG
6#%\"yGF)F)*(^#!\"\"F)-%$sinGF'F)-%%sinhGF,F)F)" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 23 "evalc((x+I*y)/(x-I*y));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,(*&*$)%\"xG\"\"#\"\"\"F),&*$F&F)F)*$)%\"yGF(F)F)!\"\"F
)*&*$F-F)F)F*F/F/*&*(^#F(F)F.F)F'F)F)F*F/F)" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 0 "" }}}}{MARK "32 1" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 
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