Complex Analysis     MATH 305

Quiz #1

Friday, Sept. 16, in class

The first quiz covers Chapter 1 of the course text. You should go over the first homework assignment (including the partial solutions available on moodle), the textbook and your class notes. The quiz will be short (10-15 minutes) and focus on basic concepts and calculations from Chapter 1. Types of possible questions include: short answer, fill in the blank, true/false, multiple choice, etc. You may also be asked to do some short calculations.

Note: No calculators are allowed on the quiz so be prepared to answer questions without your personal calculator.

The following topics and definitions are important material for the quiz. You may be asked to define some terms precisely.

  1. Complex Numbers: complex plane, addition, multiplication, basic algebraic properties, multiplicative and additive inverses, conjugate
  2. Vectors and Moduli: addition and subtraction of complex numbers vectorially, modulus of a complex number, equation of a circle using the modulus, triangle inequalities, properties of the modulus (e.g., the modulus of a product equals the product of the moduli)
  3. Complex Conjugate: properties of, connection with modulus
  4. Exponential Form: polar coordinates, Euler's formula, argument versus Argument, products and powers in exponential form, de Moivre's formula, arguments of products and quotients
  5. Roots of Complex Numbers: how to find the nth roots of a complex number, geometric description of the location of the roots, roots of unity