Other Operations of Complex numbers

Other complex operations.

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Complete Code

Download file: OtherOperations.pg

See Also

PG problem file

Explanation

DOCUMENT();

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

Preamble

These standard macros need to be loaded. 
Context('Complex');

$z0 = Complex(non_zero_random(-5, 4), non_zero_random(-5, 5));
$z1 = Complex(non_zero_random(-5, 4), non_zero_random(-5, 5));
$z2 = Complex(non_zero_random(-5, 4), non_zero_random(-5, 5));

Setup

To use complex numbers, switch to the Complex context with Context('Complex').

See the problem Basic Operations of Complex numbers for different ways of creating complex numbers.

This shows the usage of the functions Re (real part), Im (imaginary part), abs (absolute value or modulus which gives the distance from the origin), arg (the angle with the positive real axis), and conj (the complex conjugate).

BEGIN_PGML
Let [`z_0 = [$z0]`], [`z_1 = [$z1]`], and [`z_2 = [$z2]`]. Find

[`\text{Re}(z_0) =`] [___]{Re($z0)}

[`\text{Im}(z_0) =`] [_____]{Im($z0)}

[`|z_1| =`] [___]{abs($z1)}

[`\text{arg}(z_1) =`] [___]{arg($z1)}

[`\text{conj}(z_2) =`] [___]{conj($z2)}
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.