Complex Numbers

Abstract

Sum, product and quotient in cartesian and modulus-argument forms. Complex conjugate numbers. Representation of complex numbers on an Argand diagram. De Moivre’s theorem with simple applications to trigonometric identities and the roots of a number. The relation

$${e^{i\theta }} = \cos \,\theta + i\sin \,\theta $$

and its use in the rotation of vectors. Simple loci including |z − a| = k |z − b | and arg (z − a) − arg (z − b) = θ.