Exam 1 covers the same content as **Homework Sets 1–5**. Sections from the text, and the topics included, are as follows:

- Complex numbers (
**Chapter 1**)- How cubic equations lead to complex numbers (but will not be on exam!)
- Definition of complex numbers as ordered pairs of reals and of their addition and multiplication operations
- Geometric representation of complex numbers, and of their addition and multiplication
- Algebra of complex numbers
- Real part, imaginary part, conjugate; reciprocals and quotients
- Modulus, polar representation, e
and exponential form, Euler’s formula, Arg and arg^{z } - DeMoivre’s formula,
*n*th roots - Curves and their parametrization; closed and simple closed curves; Jordan curve theorem
- Open, closed, and punctured disks
- Interior and boundary points; interior, boundary, and closure of a set; bounded and unbounded sets; connected sets

- Complex functions (
**Chapter 2 except section 2.4.1;**)

Section 10.2*except*Theorem 10.3 and*except*subsection 10.2.1- Complex functions in cartesian and polar forms
- Idea of a complex function as a mapping of the plane; image of sets; one-to-one and onto functions
- Affine linear functions and their mapping properties; finding images of sets under such functions
- The
*n*th power function and the principal*n*th root function; other branches of square-root - The reciprocal function (1/
*z*); the extended complex plane and the Riemann sphere

- Limits and continuity of complex functions (
**Sections 3.1–3.2**)