## ABSTRACT

This chapter begins to study dynamical systems in the plane. It considers functions of a complex variable. The chapter begins with a review of complex numbers. The arithmetic operations of addition and multiplication are defined for complex numbers in the natural way. Geometrically, addition of complex numbers is given by the parallelogram rule for addition of vectors in the plane. Division of complex numbers is defined in a roundabout way. The complex derivative is a much different object from the Jacobian matrix studied in multivariable calculus.