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, we need to switch context with Context('Complex'). The problem Basic Operations of Complex numbers showed different ways of creating complex numbers.

This shows the functions Re (real part), Im (imaginary part), abs (absolute value or modulus – distance from the origin), arg (the angle the point is from 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

All of the answers here are placed in the {} instead of making another variable.

BEGIN_PGML_SOLUTION
Solution explanation goes here.
END_PGML_SOLUTION

ENDDOCUMENT();

Solution

A solution should be provided here.