1. Complex Numbers

2. Solve the Following 1. 2x 2 = 8 2. x 2 + 4 = 0

3. Super I

4. Imaginary Numbers i = If a is a positive real number, then is an imaginary number and

5. Examples 1. 2.

6. Simplify the following 1. 2. 3. 4.

7. Complex Numbers For any real number a and b, the number a + bi is a complex number. If b = 0, then the complex number is a real number. If a = 0, then you have a pure imaginary.

8. Complex Number System

9. Complex Number System #2

11. Adding and Subtracting Complex Numbers Add or Subtract 1. (7 – 2i) + (-3 + i) 2. (2 + 5i) – (4 – 3i) 3. (-3 + 6i) + (3 + 7i) 4. (2i – 4) – (1 + 4i) 5. (5 – 7i) + 8i

12. Powers of i So……. i = i i 2 = -1 i 3 = -i i 4 = 1

13. Powers of i #2 Simplify the following down to the lowest possible power of i. 1. i 25 2. i 100 3. i 51 4. i 18

14. Multiplication Multiply the following 1. (2i)(4i) 2. 3i(1 – 5i) 3. (2 – 3i)(4 + 5i) 4. (3 – 2i)(3 + 2i)