1. L5-9, Day 3 Multiplying Complex Numbers December 2, 2015

2. Essential Question How is multiplying complex numbers similar to multiplying polynomials that I have already learned?

3. You can multiply complex numbers by using the Distributive Property and treating the imaginary parts as like terms. Simplify by using the fact i 2 = –1.

4. Warm-up: Multiply the following polynomials: 1. 2x (5x + 8) 2. (2x – 1)(x + 2) 3. (3x – 4) 2 10x 2 + 16x 2x(x + 2) – 1(x + 2) 2x 2 + 4x – x – 2 2x 2 + 3x – 2 (3x – 4)(3x – 4) 9x 2 – 12x – 12x + 16 9x 2 – 24x + 16

5. Multiply. Write the result in the form a + bi. Example 1: Multiplying Complex Numbers –2i(2 – 4i) Distribute. Write in a + bi form. Use i 2 = –1. Replace the i 2 and simplify. –4i + 8i 2 –4i + 8(–1) –8 – 4i

6. Multiply. Write the result in the form a + bi. Example 2: Multiplying Complex Numbers (3 + 6i)(4 – i) Multiply. Write in a + bi form. Use i 2 = –1. Replace the i 2 and simplify. 12 – 3i + 24i – 6i 2 12 + 21i – 6(–1) 18 + 21i

7. Multiply. Write the result in the form a + bi. Example 3: Multiplying Complex Numbers (2 + 9i)(2 – 9i) Multiply. Write in a + bi form. Use i 2 = –1. Replace the i 2 and simplify. 4 – 18i + 18i – 81i 2 4 – 81(–1) 85 Note that these complex numbers are CONJUGATES. What kind of number is the result of multiplying conjugates?

8. Multiply. Write the result in the form a + bi. Example 4: Multiplying Complex Numbers (–5i)(6i) Multiply. Write in a + bi form. Use i 2 = –1. Replace the i 2 and simplify. –30i 2 –30(–1) 30 What kind of number results when you multiply PURE imaginary numbers?

9. Multiply. Write the result in the form a + bi. 2i(3 – 5i) You try… Distribute. Write in a + bi form. Use i 2 = –1. Replace the i 2 and simplify. 6i – 10i 2 6i – 10(–1) 10 + 6i

10. Multiply. Write the result in the form a + bi. (4 – 4i)(6 – i) You try… Distribute. Write in a + bi form. Use i 2 = –1. Replace the i 2 and simplify. 24 – 4i – 24i + 4i 2 24 – 28i + 4(–1) 20 – 28i

11. Multiply. Write the result in the form a + bi. (3 + 2i)(3 – 2i) Distribute. Write in a + bi form. Use i 2 = –1. Replace the i 2 and simplify. 9 – 6i + 6i – 4i 2 9 – 4(–1) 13 You try…

12. Assignment 2-20 EVENS on handout