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Use l() to construct URLs in Drupal.

$next_link = l('Next', 'node/' . $nids[$next]);
$previous_link = l('Previous', 'node/' . $nids[$previous]);

Indeed, it's just $z^*$ rotated by $2\theta$... And it's almost the right answer! You know that a symmetry composed with a rotation is still a symmetry, and you know that an (orthogonal) symmetry is characterized by its fixed points. So you want to get a symmetry that fixes the axis spanned by $e^{i\theta}$ (as an $\mathbb{R}$ vector space); an easy way to do that is, as you've noticed, to rotate by $-\theta$ (and not $\theta$ actually), flip over the real line (conjugation) and then rotate by $\theta$. So you get $(ze^{-i\theta})^* e^{i\theta} = z^* e^{2i\theta}$. It is easily checked that this fixes $e^{i\theta}$, and it's an orthogonal symmetry, therefore it's the one you're looking for.

FTP is a good way to upload files to a live server especially if they are static files. Even if they are php files ftp/sftp is the easy way.

There are other methods for e.g. git sync etc. But I'll assume you're just uploading regular html/php files, in which case ftp is good enough and widely used.

Filezilla is a good free ftp program to upload files to the server.

Once you have that make the connection to your server using your ftp/sftp credentials. I would recommend using sftp as that is secure.

Once you're connected locate your public_html folder and just transfer all your files there overwriting any index.html files. Be sure to name your homepage index.html or index.php as most servers are configured to run that as the index file.

If your index file is inside a directory, place it outside of that and into your public_html to avoid http://example.com/dir/index.html

Hope that helps.