1. 5.7.2 – Complex Numbers

2. From yesterday, we learned the application of the imaginary unit i Used for problems such as; -5x 2 = 20

3. Complex Number As part of the imaginary numbers and the imaginary number system, we have what are known as Complex Numbers What does the word complex mean? a + bi a = real number bi = imaginary number

4. Combining Complex Numbers Similar to like variables (2x, 10x, -x) and like powers (x 4, 10x 4 ), we may combine line terms from complex numbers To add or subtract complex numbers, we do the following 1) Combine the real parts with real parts 2) Combine the imaginary parts with imaginary parts

5. Example. Simplify the following expressions 1) (2 + 5i) + (3 + 10i) 2) (-9 – 4i) + 10i 3) -13i – (4 + 6i) 4) 19i – 5i + 2

6. Multiplication With multiplication, we will treat them as a previous problem we have already done What does the problem (2 + 5i)(1 + i) resemble? Is there a previous method we can use to help us?

7. May use “FOIL” or the punnett square method Example. Find the product of the two complex numbers; (2 + 5i)(1 + i)

8. Example. Find the product of the two complex numbers; (3 - 2i)(3 + 2i)

9. Example. Find the product of the two complex numbers; (-4 - i)(-4 + 4i)

10. Example. Find the product of the two complex numbers; (i + 3) 2

11. Complete the following problems with your neighbors. We will check answers in 5 minutes. Simplify each of the following expressions. 1) 2 + 4i + 17 – 6i 2) (9 + 7i) – (4 – 5i) 3) (2 + i)(7 – 3i) 4) (6 + 2i)(1 + 2i)

12. Assignment Pg. 265 27 – 49 odd