#grouptheory #linearalgebra #matrices #representationtheory #complexnumbers Consider supporting us on Patreon: You'll get early access to all videos, and you get to watch exclusive content that will never be published on Youtube. How can the complex numbers be represented as matrices? This is an excellent warm-up for more general matrix representations later. We look at complex conjugates, the trivial representation, the determinant, and much more. Many thanks to professor Karel Dekimpe from the university of Leuven for helping me understand representations and characters. 0:00 Integer powers of i 3:52 Rational powers of i 6:47 Real powers of i 8:41 The entire complex plane 10:48 How the real numbers are represented 11:32 Reflections & complex conjugation 13:38 Degrees of freedom 17:48 The trivial representation This video is published under a CC Attribution license ( )