This lecture is part of an online undergraduate course on complex analysis. We review the basic arithmetic of complex numbers, and given some applications to some problems in number theory related to sums of two squares. At the end we briefly cover the quaternions. For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj537_iYA5QrvwhvMlpkJ1yGN