1. Precalculus Mr. Ueland 2 nd Period Rm 156

2. Today in PreCalculus Announcements/Prayer New material: Sec 2.5b, “Complex Numbers” Continue working on Assignment 22

3. Complex Solutions to Quadratics Definition: the square root part of the Quadratic Formula,, is known as the discriminant. 1.If the discriminant > 0, there are two real, distinct solutions. 2.If the discriminant = 0, there is one real, repeated solution. 3.If the discriminant < 0, there is a complex conjugate pair of solutions (i.e. x = a ± bi)

4. Example 5 Solve There are two complex conjugate solutions

5. Graphing in the Complex Plane Complex numbers can be graphed in the complex plane, with the real part graphed as the independent variable (x), and the imaginary part as the dependent variable (y).

6. Example 6 Plot u = 1 + 3i, v = 2 – i and u + v in the complex plane.

7. The Modulus of a Complex Number The absolute value or modulus of a complex number z is defined as it’s distance from the origin.

8. Example 7 Find the distance between u = –4 + i and v = 2 + 5i

9. Assignment 22 Read: pp 221-226 Do: pp 227-228/1-39 eoo, 41-44, 45-53 odd, 55-60, 62 (2 pts), 63 (2 pts), 69a (28 problems) Due: Tomorrow at the start of class