1. 10/18/20159-6 9-6 Complex Numbers

2. Solve: Solve: 10/18/20159-6

3. 10/18/20159-6 Imaginary Numbers Imaginary Number: Simplifying Imaginary Numbers:

4. 10/18/20159-6 Complex Numbers Complex numbers: Complex numbers: When a real number is combined with an imaginary number - a number in the form of a + bi where: a is the real parta is the real part bi is the imaginary partbi is the imaginary part

5. 10/18/20159-6 Operations on Complex Numbers Let x = 3 + 2i and y = 1 – 3i. Find: a)x + y: b)x – y: c)xy: So: Treat “i ” like a variable and follow all algebra rules.

6. Factoring: The difference of perfect squares… Factor the following: 10/18/20159-6 These are an example of Complex Conjugates.

7. Where do we find complex conjugates? Solve the following equation: 10/18/20159-6

8. Other stuff… Factor Theorem still holds true: If “i ” is a solution, then (x – i) is a factor. (and vise-versa) All real numbers can be written as complex numbers, and so can imaginary numbers: ex: 4i = 0 + 4i ex: 2 = 2 + 0i 10/18/20159-6