1. SFM Productions Presents: Another sleep deprived 45 minutes in your Villa Walsh Pre-Calculus experience! 2.4Complex Numbers

2. Homework for section 2.4 p164 #9-19, 25-29, 35-39, 43-45, 51-57, 63-77

3. The imaginary unit: i Solve, using real numbers: x 2 + 1 = 0 Mathematicians got tricky and created an expanded number system, which included: i. i is defined as follows:

4. Real numbers combined with multiples of this imaginary unit are known as the: Set of Complex Numbers The STD form of a complex number is: a + bi Real partImaginary part

5. If b = 0, then a + bi = aand a therefore is a real number. If a = 0, then a + bi = biand bi therefore is a pure imaginary number. If b = 0, then a + bi is an imaginary number. EVERY number can be written as a complex number. Example: 4 = 4 + 0i

6. Sum and Difference of complex numbers. Examples

7. Multiplication of complex numbers. Examples Note: after foiling, if you have an i 2, you must change it to a (-1) and multiply as needed.

8. Complex conjugates and division Doing this is along the same line as rationalizing the denominator - it cleans up the denominator so that the denominator is a real, rational number.

9. Examples

10. Pull out the -1 first…THEN do whatever the math has you do. Complex Solutions of Quadratic Functions Example

12. The different powers of i …and so on.

14. Go! Do!