1. 2.2 Complex Numbers Fri Feb 20 Do Now 1) 2x^2 -8 = 0 2) (sinx)^2 – 2sinx + 1 = 0

2. Quiz Review Retakes by Thursday

3. The number i The number i is defined such that and

4. Ex Express each number in terms of I 1) 2) 3)

5. Complex Numbers A complex number is a number of the form a + bi, where a and b are real numbers. The number a is said to be the real part and the number b is said to be the imaginary part

6. Addition and Subtraction When adding and subtracting complex numbers, combine the real parts together and the imaginary parts together

7. Ex Simplify the following expressions 1) (8 + 6i) + (3 + 2i) 2) (4 + 5i) – (6 – 3i)

8. Multiplication Complex numbers follow the same multiplication rules Remember: i^2 = -1

9. Ex Simplify each of the following 1) 2) 3)

10. Powers of i Let’s look at the first 8 powers of I Notice how the same 4 values cycle!

11. Ex Simplify each of the following 1) i^37 2) i^58 3) i^75 4) i^80

12. Conjugates and Division The conjugate of a complex number a + bi is a – bi These are considered complex conjugates Use complex conjugates to simplify rational expressions involving complex numbers

13. Ex Divide 2 – 5i by 1 – 6i

14. Closure Simplify i^24 HW: p.198 #1-9 odds, 11-73 EOO, 75-83 odds