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

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

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.

Example 1: Simplify (exact values):

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

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

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

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

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

Example 7: Factor over the set of complex numbers: (a) x (b) 4x

Closure Factor over the set of complex numbers.