1. January 17, 2012 At the end of the today, you will be able to work with complex numbers. Warm-up: Correct HW 2.3: Pg. 160 #57-62 57. (2x – 1)(x + 2)(x – 1); x = 1/2, -2, 1 58.(3x – 1)(x + 3)(x – 2); x = 1/3, -3, 2 59. (x – 1)(x – 2)(x – 5)(x + 4); x = 1, 2, 5, -4 60. (4x + 3)(2x – 1)(x + 2)(x – 4); x = -3/4, 1/2, -2, 4 61. (x + 7)(2x + 1)(3x – 2); x = -7, -1/2, 2/3 62. (x – 3)(2x + 5)(5x – 3); x = 3, -5/2, 3/5 HW 2.4: Pg. 167 #20-21, 27-29, 46- 49, 55, 65, 67

2. Lesson 2.4 Complex Numbers - Adding real numbers to real multiples of imaginary numbers is written as a + bi in standard form a + bi Combining complex numbers is like combining like terms in a polynomial. Example 1: (4 + 7i) – (1 – 6i) = 4 – 1 + 7i + 6i = 3 + 13i a represents the real part of the complex number bi represents the imaginary part of the complex number Make sure your answer is written in standard form!

3. Multiplying Complex Numbers Powers of i i 1 = i 2 = i 3 = i 4 = i 5 = i 6 = i 7 = i 8 = -i-i 1 i -i-i 1 Example 2: (2 – i)(4 + 3i) 8 + 6i - 4i- 3i 2 8 + 2i – 3(-1) 8 + 2i + 3 = 11 + 2i

4. Practice simplifying complex numbers 1.(-1 + 2i) + (4 + 2i) 2.(3 + 2i) 2 3.(3 + 2i)(3 – 2i) *These are called conjugates!

5. Writing Quotients in Standard Form Example 3: Write in standard form *Cannot have a radical in the denominator, so rationalize by using the conjugate. 16 – (-4) *Write in standard form

6. Complex solutions of a Quadratic Equation Solve the quadratic using the quadratic formula, then write the result in standard form. Example 4: 3x 2 – 2x + 5 = 0