1. Chapter 5.9 Complex Numbers

2. Objectives To simplify square roots containing negative radicands. To solve quadratic equations that have pure imaginary solutions. To add, subtract, and multiply complex numbers. Why is this important? You can use complex numbers to solve problems involving electricity and physics.

3. Definition of Pure Imaginary Numbers

4. Example

5. Simplify

6. Example Simplify:i 25 Answer: i

7. Example Solve: 4x 2 + 26 = 0 Answer: x = ±3i

8. Definition of Equal Complex Numbers a + bi = c + di if and only if a = c and b = d Two complex numbers are equal is and only is their real parts are equal and their imaginary parts are equal.

9. Examples Simplify the expression: (8 – 5i) + (2 + i) Answer: 10 – 4i Simplify: (4 + 2i)(3 – 5i) Answer: 22 – 14i

10. Practice p. 314 numbers 6-18 (even)