1. Do Now What is the exact square root of 50? What is the exact square root of -50?

2. Chapter 9: Polynomial Functions Lesson 6: Complex Numbers Mrs. Parziale

3. Complex Numbers: is an imaginary number (i). A complex number has the form (a+bi) where a is the real part, b = imaginary part. Both a and b are real numbers. The expressions (a+bi) and (a-bi) are complex conjugates. When you multiply them you get a real number.

4. Example 1: Simplify (exact values):

5. Example 2: Multiply: (3+5i)(2-i)

6. Example 3: Multiply (3+i)(3-i)

7. Example 4: Rewrite in a + bi form. Let z = 2+3i and w = 1-5i (a) 4z (b) 2z – 3w

8. Example 5: Write in a+bi form (rationalize the denominator):

9. Example 6: Factor x 2 – 5over the set of polynomials with real coefficients (not only integers):

10. Example 7: Factor over the set of complex numbers: (a) x 2 + 9 (b) 4x 2 + 16

11. Closure Factor over the set of complex numbers.