Roots of unity: Difference between revisions

Content added Content deleted
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{{libheader|Math::Complex}}
{{libheader|Math::Complex}}
<perl>use Math::Complex;
<perl>use Math::Complex;

foreach $n (1 .. 10) {
foreach $n (2 .. 10) {
printf "%2d ", $n;
printf "%2d", $n;
foreach $k (1 .. $n) {
foreach $k (1 .. $n/2) {
$ret = cplxe(1, 2 * pi * $k / $n);
$ret = cplxe(1, 2 * pi * $k / $n);
$ret->display_format('style' => 'cartesian', 'format' => '%.3f');
$ret->display_format('style' => 'cartesian', 'format' => '%.3f');
print "($ret)";
print " $ret";
}
}
print "\n";
print "\n";
}</perl>
}</perl>

Output:
Output:
<pre>
<pre>
1 (1.000-0.000i)
2 -1.000+0.000i
2 (-1.000+0.000i)(1.000-0.000i)
3 -0.500+0.866i
3 (-0.500+0.866i)(-0.500-0.866i)(1.000-0.000i)
4 0.000+1.000i -1.000+0.000i
5 0.309+0.951i -0.809+0.588i
4 (0.000+1.000i)(-1.000+0.000i)(-0.000-1.000i)(1.000-0.000i)
5 (0.309+0.951i)(-0.809+0.588i)(-0.809-0.588i)(0.309-0.951i)(1.000-0.000i)
6 0.500+0.866i -0.500+0.866i -1.000+0.000i
7 0.623+0.782i -0.223+0.975i -0.901+0.434i
6 (0.500+0.866i)(-0.500+0.866i)(-1.000+0.000i)(-0.500-0.866i)(0.500-0.866i)(1.000-0.000i)
7 (0.623+0.782i)(-0.223+0.975i)(-0.901+0.434i)(-0.901-0.434i)(-0.223-0.975i)(0.623-0.782i)(1.000-0.000i)
8 0.707+0.707i 0.000+1.000i -0.707+0.707i -1.000+0.000i
9 0.766+0.643i 0.174+0.985i -0.500+0.866i -0.940+0.342i
8 (0.707+0.707i)(0.000+1.000i)(-0.707+0.707i)(-1.000+0.000i)(-0.707-0.707i)(-0.000-1.000i)(0.707-0.707i)(1.000-0.000i)
9 (0.766+0.643i)(0.174+0.985i)(-0.500+0.866i)(-0.940+0.342i)(-0.940-0.342i)(-0.500-0.866i)(0.174-0.985i)(0.766-0.643i)(1.000-0.000i)
10 0.809+0.588i 0.309+0.951i -0.309+0.951i -0.809+0.588i -1.000+0.000i
10 (0.809+0.588i)(0.309+0.951i)(-0.309+0.951i)(-0.809+0.588i)(-1.000+0.000i)(-0.809-0.588i)(-0.309-0.951i)(0.309-0.951i)(0.809-0.588i)(1.000-0.000i)
</pre>
</pre>


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