SAMPLE College Algebra

Chapter 3: Quadratics II and Complex Numbers

OVERVIEW The sections of this chapter are: 3.1 The Quadratic Formula 3.2 Completing the Square 3.3 Visual Complex Numbers

3.4 Complex Conjugation is Simple! 3.5 Complex Number Operations 3.6 Complex Quadratic Equations A quadratic equation has been discussed and demonstrated. In the previous chapter the following methods were applied to solve quadratic equations: • Sign recognition • ACmethod • Factoring formulas It has been emphasized that solving quadratic equations means finding points where the quadratic equation is equal to zero. Solutions to quadratic equations are also called zeros or roots. It may be necessary to make use of some additional methods to solve quadratic equations. In this chapter, additional methods of solving quadratic equations will be applied to solve quadratic equations: • Quadratic formula • Square root property • Completing the square It will be eye-opening to take a look at complex numbers in a visual way. Complex numbers can be useful in powerful ways, but there is an approach to complex numbers that can be quite simple . Complex numbers help with some interesting and mysterious behavior and phenomena, that shows up every day in the world around us. With complex numbers it is possible to: • Implement 3-D video games • Design with inductors and capacitors that are found in almost all electronic devices

• Describe different characteristics of light • Understand audio amplifiers and speakers • Describe power and electricity usage in homes and businesses • Understand medical equipment and sensors OBJECTIVES By the end of the chapter, a student will be able to: • Apply the quadratic formula to solve quadratic equations • Apply the square root property to solve quadratic equations