** Using WeBWorK **

Using cplx_cmp and mode=>'strict' seems to do what I want, but shouldn't I be using cmp instead?

This is a different problem than above (and still being developed.)

DOCUMENT(); # This should be the first executable line in the problem.

loadMacros(
"PG.pl",
"PGbasicmacros.pl",
"MathObjects.pl",
"PGanswermacros.pl",
"PGauxiliaryFunctions.pl",
"PGcomplexmacros.pl",
"unionLists.pl"
);

TEXT(beginproblem());

######################################
# Setup

Context("Complex");

# create random variables
$a = non_zero_random( 11, 70, 7 );
$b = non_zero_random( 11, 70, 11 );
$c = non_zero_random( 11, 70, 5);

# Calculate the answers
for ( $n = 0; $n <= 9; $n++ )
{
$answer[$n] = (new Complex(0,1) )**$n;
}



BEGIN_TEXT
Calculate the following:$PAR
(a) \(i^0\ =\) \{ans_rule(5)\} $PAR
(b) \(i^1 =\) \{ans_rule(5)\} $PAR
(c) \(i^2\ =\) \{ans_rule(5)\} $PAR
(d) \(i^3\ =\) \{ans_rule(5)\} $PAR
(e) \(i^4\ =\) \{ans_rule(5)\} $PAR
(f) \(i^5\ =\) \{ans_rule(5)\} $PAR
(g) \(i^6\ =\) \{ans_rule(5)\} $PAR
(h) \(i^7\ =\) \{ans_rule(5)\} $PAR
(i) \(i^8\ =\) \{ans_rule(5)\} $PAR
(j) \(i^9\ =\) \{ans_rule(5)\} $PAR
END_TEXT

# Check answers
# Use cplx_cmp and mode => 'strict' so they can't enter things like i^3

for ( $n = 0; $n <= 9; $n++ )
{
ANS(cplx_cmp( $answer[$n], mode=>'strict' ) );
}

# ANS($answer[$n]->cmp);


$showPartialCorrectAnswers = 1;

ENDDOCUMENT(); # This should be the last executable line in the problem.

Here are the issues: when you use Context("LimitedComplex") all your computations are done in that context, so you are restricted to its limitations just as a student is. One reason for this is so that the correct answer that you give for the student will actually be something the student can type. Without this, for example, your

    $answer[0] = Complex("conj($a)");

would make the correct answer show as conj(3+2i), which the student could not type. (Remember that Compute() not only computes the value, but also sets the correct answer to be the string you originally used to get the answer.)

The second issue is that adding

    Context("LimitedComplex");

does not affect any existing values, so all the numbers you already created are still in the Complex context. Remember that answers are checked using the context where the correct answer was created (not the currently active context), so switching to LimtedComplex but using ANS() with a value in the Complex context doesn't use the LimitedComplex context. That's why students can still enter conj() in their answers.

So if you need to do computation that the student won't be able to do, do that in Context("Complex") as you are, but you need to move your results from the Complex to the LimitedComplex context. One way to do that is

    Context("Complex");
    $a = Complex(non_zero_random(-5,5,1), random(1,10,1));
    $z = conj($a);
    Context("LimitedComplex");
    $answer = Compute($z->string);

Here you do the computations before setting LimtedComplex, and then call Compute() again to re-parse the answer in the new context.