Complex Numbers, Limited Input

This shows the capabilities of the LimitedComplex context.

Complete Code

POD for Macro Files

contextLimitedComplex.pl

PG problem file

Explanation

DOCUMENT();

loadMacros(
    'PGstandard.pl',            'PGML.pl',
    'contextLimitedComplex.pl', 'PGcourse.pl'
);

Preamble

This problems shows the capabilities of the contextLimitedComplex.pl macro, so it must be loaded.

Context('LimitedComplex');

$x0 = non_zero_random(-5, 5);
$y0 = non_zero_random(-5, 5);
$x1 = non_zero_random(-5, 5);
$y1 = non_zero_random(-5, 5);

$z0 = Complex($x0, $y0);
$z1 = Complex($x1, $y1);

$ans1 = $z0 + $z1;
$ans2 = $z0 * $z1;

$arg0 = atan($y0 / $x0) + ($x0 > 0 ? ($y0 > 0 ? 0 : 2 * pi) : pi);
$arg1 = atan($y1 / $x1) + ($x1 > 0 ? ($y1 > 0 ? 0 : 2 * pi) : pi);
$abs0 = sqrt($x0**2 + $y0**2);
$abs1 = sqrt($x1**2 + $y1**2);

Setup

Often when students are asked to perform operations with complex numbers, usually it is not desirable for them to be able to enter those operations in their answer. One way to achieve this is by using the LimitedComplex context via Context('LimitedComplex'). This context will only allow a simplified complex number in either Cartesian or polar form to be entered. Note that Perl operations on complex numbers are still allowed, but operations in a string passed to the Compute call or in a student answer are not.

If you only want complex numbers to be entered in Cartesian form you can use Context('LimitedComplex-cartesian') and if you only want students to enter numbers in polar form use Context('LimitedComplex-polar').

The final computation determines the polar form of the answer for use in the solution. In the LimitedComplex context, most functions are disabled, so the computations are performed on the real and imaginary components directly.

BEGIN_PGML
Let [`z_0 = [$z0]`] and [`z_1 = [$z1]`]. Find

[`z_0 + z_1 =`] [___]{$ans1}

[`z_0 z_1 =`] [___]{$ans2}

Give the answers in simplified Cartesian or polar form.
END_PGML

Statement

This is the problem statement in PGML.

BEGIN_PGML_SOLUTION
The first answer in Cartesian form is [`[$ans1]`].

The second answer in polar form is
[`[@ Round($abs0 * $abs1, 4) @] e^{[@ Round($arg0 + $arg1, 4) @]i}`].
END_PGML_SOLUTION

ENDDOCUMENT();

Solution

Note that a solution should do better than is demonstrated here. Don’t just give the answers. Show how to find the answers.