2.2 Complex Numbers Day 1

1. 2.2 Complex NumbersDay 1 Do Now Solve the equations 2x^2 -8 = 0 (sinx)^2 – 2sinx + 1 = 0

2. The number i • The number i is defined such that and

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

4. 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

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

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

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

8. Ex • Simplify each of the following • 1) • 2) • 3)

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

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

11. 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

12. Ex • Divide 2 – 5i by 1 – 6i

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