# π Computing the distance between two points using Perl 6

Calculate the distance between the two points on a surface.

There are two points on a surface, each with their own coordinates, xand y. The task is to find the distance between these two points.

A straightforward solution would be to use the Pythagorean theorem:

my (\$x1, \$y1) = (10, 3);
my (\$x2, \$y2) = (9, 1);
say sqrt((\$x1 - \$x2) ** 2 + (\$y1 - \$y2) ** 2);

This works, but it requires a lot of typing. In Perl 6, there is a slightly easier way if you use complex numbers.

my \$a = 10+3i;
my \$b = 9+1i;
say (\$a - \$b).abs;

The result of both programs is the same. Complex numbers are objects of theΒ Complex data type and are introduced viaΒ iβthe imaginary unit:

The result of the differenceΒ \$a - \$b is also a complex number, and theΒ abs method can be called on it. This method returns the absolute value of a complex number, which is actually the distance between the two points.

Notice the style:Β 10+3i vs.Β 10 + 3i. The first one seems to be preferable as it is also used as the default output format by the compiler. The second option may be confusing when a complex number is used in an expression with other variables or numbers.

\$ perl6 -e'say (10+3i, -i, 4i, 10+0i)'
(10+3i -0-1i 0+4i 10+0i)