** Using WeBWorK **

For complex numbers you would use LimitedComplex, not LimitedNumeric. One of your questions asked about numbers like 3*7, and in that case, you would use LimitedNumeric. Also, the title of the question is about numbers.

Are you using the newest version of contextComplexJ.pl from the develop branch, or the older one in the master branch? It has been completely rewritten. The older one only operates on the standard Complex context, not other contexts. The new one can be enabled in any context with complex numbers.

If you are using the new one, you can add

context::ComplexJ->Enable();

Note that, since you are using j explicitly in your problem, there is no point in conditionally loading contextComplexJ.pl, as the problem will fail without it. The new contextComplexJ.pl is set up to allow you to set your course default in PGcourse.pl without having to modify the problem files themselves, but you have to write your problems using i notation originally in order to allow PGcourse.pl to have proper control over the results.

Unfortunately, the LimitedComplex context isn't included in the ones that contextComplexJ.pl modifies automatically, so you need to do that by hand with the command above. Here is one example:

 loadMacros(
   "PGstandard.pl",
   "MathObjects.pl",
   "PGgraphmacros.pl",
   "contextComplexJ.pl",
   "contextLimitedComplex.pl", 
   "PGcourse.pl",
 ) ;

$showPartialCorrectAnswers=1;
TEXT(beginproblem());

Context("Complex");

$z1 =random(1,7,1) + non_zero_random(-7,7,1)*j;
$z2 = random(-7,-1,1) + non_zero_random(-7,7,1)*j;
 
Context("LimitedComplex-cartesian");
context::ComplexJ->Enable();

$z3 = Compute($z1*$z2);

Context()->texStrings;
BEGIN_TEXT
$BBOLD Multiplication of  complex numbers. $EBOLD 
$PAR
The product of two complex numbers, \(z_1 = x_1 + j y_1\)
and \(z_2 = x_2 + j y_2\) is defined by
\(z_1 z_2 =  (x_1 x_2 - y_1 y_2) +  j (x_1 y_2 + x_2 y_1)\), 
where the usual rules of multiplication of numbers apply and 
make use of the fact that \(j^2=-1\). 
$PAR
Consider the two complex numbers \(z_1  = $z1\) and \(z_2  = $z2\).
$PAR
Compute the product \(z_1 z_2 =\)\{ans_rule(10)\}.
END_TEXT
Context()->normalStrings;
 
ANS($z3->cmp);

The error messages from the LimitexComplex contexts will use i rather than j (e.g., "Your answer should be if the form a+bi"), so you may want to use Context()->{error}{msg} to remap those errors to use j instead.

I also added Context()->texStrings; and Context()->normalStrings around your BEGIN_TEXT/END_TEXT block to avoid extra parentheses around the complex numbers when they are inserted into the text.

You should also note that your <if ram> is going to cause problems when students try to get a hardcopy of your homework set. It is never a good idea to insert raw HTML into a problem for that reason. Also, as you write problems, you should always test them in hardcopy to make sure nothing goes wrong (it is easy for the output to work on screen but not in hardcopy).