I am designing a problem to use Euler's formula to convert from polar complex to rectangular complex. The computation is simple but I'm having trouble with the display
The command
$f11 = Formula(" $r1 e**(i *pi/$frac_theta1) ")->reduce;
works fine but I want to display the formula in Tax mode
in the text section, if I write
Write \( z_2 = $r2 e^{j \pi/$frac_theta2} = $r2 exp(j \pi/$frac_theta2) \)
I get the symbol pi and the fraction I want but when $frac_theta2 is negative, it puts -2 in the denominator. If I try to print $f11, then I don't get the exponential notation but the ^ symbol
How do I produce a simplified (reduced) formula in Tex?
Code follows
## Complex Numbers and the Complex Plane
## ENDDESCRIPTION
## KEYWORDS('Complex', 'Plane')
## Tagged by nhamblet
## DBsubject('Algebra')
## DBchapter('Equations and Inequalities')
## DBsection('Complex Numbers')
## Date('')
## Author('')
## Institution('Rochester')
## TitleText1('')
## EditionText1('')
## AuthorText1('')
## Section1('')
## Problem1('')
DOCUMENT() ;
loadMacros(
"PGstandard.pl",
"MathObjects.pl",
"PGcourse.pl"
) ;
#sub i (); #make i act like the imaginary unit.
$showPartialCorrectAnswers=1;
TEXT(beginproblem()) ;
$r1 =random(1,9,1);
do {$r2 = random(2,9,1);} until ($r2 != $r1);
$frac_theta1 = list_random(0,-2,2,-3,3,-4,4,-6,6);
do {$frac_theta2 = list_random(0,-2,2,-3,3,-4,4,-6,6);} until ($frac_theta2 != $frac_theta1);
$theta1 = pi/$frac_theta1;
$theta2 = pi/$frac_theta2;
$x1 = cos($theta1);
$y1 = sin($theta1);
$x2 = cos($theta2);
$y2 = sin($theta2);
Context("Complex");
$f11 = Formula(" $r1 e**(i *pi/$frac_theta1) ")->reduce;
$f12 = Formula("$r1 exp(i *pi/$frac_theta1) ")->reduce;
$f21 = Formula(" $r2 e**(i *pi/$frac_theta2) ")->reduce;
$f22 = Formula("$r2 exp(i *pi/$frac_theta2) ")->reduce;
BEGIN_TEXT
Using Euler's formula
\[ e^{i\theta} =\cos(\theta) + i \sin(\theta). \]
$PAR
Write \(z_1 = \)$f11 = $f12 in rectangular coordinates $BR
\(z_1 =\)\{ans_rule(10)\} + j\{ans_rule(10)\}
$PAR
Write \( z_2 = $r2 e^{j \pi/$frac_theta2} = $r2 exp(j \pi/$frac_theta2) \) $BR
$f21 $f22 $BR
\(z_2 =\)\{ans_rule(10)\} + j\{ans_rule(10)\}
END_TEXT
ANS num_cmp($x1 );
ANS num_cmp($y1);
ANS num_cmp($x2);
ANS num_cmp($y2);
ENDDOCUMENT() ;
Formula (MathObjects) recognizes exp as the exponential function, but latex does not. Latex requires \exp.
On the other hand, for latex to interpret formulas correctly, you need to add texStrings to the context.
Here I have modified your code. See highlighting below. Both MathObjects and latex work nicely.
## Complex Numbers and the Complex Plane
## ENDDESCRIPTION
## KEYWORDS('Complex', 'Plane')
## Tagged by nhamblet
## DBsubject('Algebra')
## DBchapter('Equations and Inequalities')
## DBsection('Complex Numbers')
## Date('')
## Author('')
## Institution('Rochester')
## TitleText1('')
## EditionText1('')
## AuthorText1('')
## Section1('')
## Problem1('')
DOCUMENT() ;
loadMacros(
"PGstandard.pl",
"MathObjects.pl",
"PGcourse.pl"
) ;
#sub i (); #make i act like the imaginary unit.
$showPartialCorrectAnswers=1;
TEXT(beginproblem()) ;
$r1 =random(1,9,1);
do {$r2 = random(2,9,1);} until ($r2 != $r1);
$frac_theta1 = list_random(0,-2,2,-3,3,-4,4,-6,6);
do {$frac_theta2 = list_random(0,-2,2,-3,3,-4,4,-6,6);} until ($frac_theta2 != $frac_theta1);
$theta1 = pi/$frac_theta1;
$theta2 = pi/$frac_theta2;
$x1 = cos($theta1);
$y1 = sin($theta1);
$x2 = cos($theta2);
$y2 = sin($theta2);
Context("Complex");
$f11 = Formula(" $r1 e**(i *pi/$frac_theta1) ")->reduce;
$f12 = Formula("$r1 exp(i *pi/$frac_theta1) ")->reduce;
$f21 = Formula(" $r2 e**(i *pi/$frac_theta2) ")->reduce;
$f22 = Formula("$r2 exp(i *pi/$frac_theta2) ")->reduce;
Context()->texStrings; # adds tex string capability to the context
BEGIN_TEXT
Using Euler's formula
\[ e^{i\theta} =\cos(\theta) + i \sin(\theta). \]
$PAR
Write \(z_1 = $f11 = $f12\) in rectangular coordinates $BR
\(z_1 =\)\{ans_rule(10)\} + j\{ans_rule(10)\}
$PAR
Write \( z_2 = $r2 e^{j \pi/$frac_theta2} = $r2 \exp(j \pi/$frac_theta2) \) $BR
\(z_2 =\)\{ans_rule(10)\} + j\{ans_rule(10)\}
END_TEXT
ANS num_cmp($x1 );
ANS num_cmp($y1);
ANS num_cmp($x2);
ANS num_cmp($y2);
ENDDOCUMENT() ;
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You are logged in as Murphy Waggoner (Logout)
UsingWW
On the other hand, for latex to interpret formulas correctly, you need to add texStrings to the context.
Here I have modified your code. See highlighting below. Both MathObjects and latex work nicely.
## Complex Numbers and the Complex Plane
## ENDDESCRIPTION
## KEYWORDS('Complex', 'Plane')
## Tagged by nhamblet
## DBsubject('Algebra')
## DBchapter('Equations and Inequalities')
## DBsection('Complex Numbers')
## Date('')
## Author('')
## Institution('Rochester')
## TitleText1('')
## EditionText1('')
## AuthorText1('')
## Section1('')
## Problem1('')
DOCUMENT() ;
loadMacros(
"PGstandard.pl",
"MathObjects.pl",
"PGcourse.pl"
) ;
#sub i (); #make i act like the imaginary unit.
$showPartialCorrectAnswers=1;
TEXT(beginproblem()) ;
$r1 =random(1,9,1);
do {$r2 = random(2,9,1);} until ($r2 != $r1);
$frac_theta1 = list_random(0,-2,2,-3,3,-4,4,-6,6);
do {$frac_theta2 = list_random(0,-2,2,-3,3,-4,4,-6,6);} until ($frac_theta2 != $frac_theta1);
$theta1 = pi/$frac_theta1;
$theta2 = pi/$frac_theta2;
$x1 = cos($theta1);
$y1 = sin($theta1);
$x2 = cos($theta2);
$y2 = sin($theta2);
Context("Complex");
$f11 = Formula(" $r1 e**(i *pi/$frac_theta1) ")->reduce;
$f12 = Formula("$r1 exp(i *pi/$frac_theta1) ")->reduce;
$f21 = Formula(" $r2 e**(i *pi/$frac_theta2) ")->reduce;
$f22 = Formula("$r2 exp(i *pi/$frac_theta2) ")->reduce;
Context()->texStrings; # adds tex string capability to the context
BEGIN_TEXT
Using Euler's formula
\[ e^{i\theta} =\cos(\theta) + i \sin(\theta). \]
$PAR
Write \(z_1 = $f11 = $f12\) in rectangular coordinates $BR
\(z_1 =\)\{ans_rule(10)\} + j\{ans_rule(10)\}
$PAR
Write \( z_2 = $r2 e^{j \pi/$frac_theta2} = $r2 \exp(j \pi/$frac_theta2) \) $BR
\(z_2 =\)\{ans_rule(10)\} + j\{ans_rule(10)\}
END_TEXT
ANS num_cmp($x1 );
ANS num_cmp($y1);
ANS num_cmp($x2);
ANS num_cmp($y2);
ENDDOCUMENT() ;
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You are logged in as Murphy Waggoner (Logout)
UsingWW
Thanks!! - BTW - after looking at the result I worried that the size of the exponent made it hard to read. I found that using the standard Latex enlarge for font size works.
Write \( {\Large z_1 = $f11 = $f12} \) in rectangular coordinates $BR
You should probably also add
Context()->normalStrings();
after the END_TEXT. It is not strictly necessary in this case, but is good practice and will avoid potential problems in later parts of the problem (if you use MathObjects in strings after the END_TEXT).