1.  Solve the equation.  1.) 3x 2 + 8 = 23  2.) 2(x + 7) 2 = 16 Warm Up

2. 4.6 Perform Operations with Complex Numbers, part 1 Algebra II

3.  Perform operations with complex numbers. Objective

4.  Imaginary unit i – i = √-1. Note that i 2 = -1.  Complex number – in standard form, a number a + bi where a and b are real numbers, a is the real part and bi is the imaginary part  Imaginary number – if b ≠ 0 then a + bi. If a = 0 and b ≠ 0 then a + bi is a pure imaginary number. Vocabulary

5.  Solve 2x 2 + 18 = -72. Example 1 – Solve a quadratic equation

6.  To add (or subtract) two complex numbers, add (or subtract) their real parts and their imaginary parts separately.  Sum of complex numbers: (a + bi) + (c + di) = (a + c) + (b + d)i  Difference of complex numbers: (a + bi) – (c + di) = (a – c) + (b – d)i Sum and Differences of Complex Numbers

7.  Write the expression as a complex number in standard form.  A.) (12 – 11i) + (-8 + 3i)  B.) (15 – 9i) – (24 – 9i)  C.) 35 – (13 + 4i) + i Example 2 – Add and subtract complex numbers

8.  Write the expression as a complex number in standard form.  A.) -5i(8 – 9i)  B.) (-8 + 2i)(4 – 7i) Example 3 – Multiply complex numbers

9.  Pg. 279 (3 – 19 first 2 columns) Assignment