Complex Numbers, Limited Input

This shows the capabilities of the LimitedComplex context.

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Complete Code

Download file: LimitedComplex.pg

POD for Macro Files

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;

# Determine the polar form of the answer to give a hint.  Since in
# LimitedComplex, most functions are diasbled, so we work on the components.
$arg0 = atan($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

If we ask students to do operations with complex numbers, often we don’t want those operations to be allowed in the answer. In this case we set the Context('LimitedComplex'). If we define complex numbers, then perl operations will be allowed, but not operations in Compute functions.

LimitedComplex will allow a single number entered (technically only one value of i) in either cartesian or polar form. This problem gives the answer in polar to check that form.

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').

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

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

[`z_0z_1=`] [___]{$ans2}

You may not enter operations between numbers for these answers.  However,
if you want the polar form (the second answer is [`[@ $abs0*$abs1 @] e^{[@ $arg0+$arg1 @]i}`])

END_PGML

Statement

This is the problem statement in PGML. 
BEGIN_PGML_SOLUTION
Solution explanation goes here.
END_PGML_SOLUTION

ENDDOCUMENT();

Solution

A solution should be provided here.