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Factor and Solve (5 minutes) 2 2 16 x 9 0 x 6x 9 0 ( x 3)( x 3) x3 x3 12 x x 1 0 2 (4 x 3)(4 x 3) 3 3 x x 4 4 18 x 12 x 0 2 (4 x 1)(3 x 1) 6 x(3 x 2) 1 x 4 2 x0 x 3 1 x 3 Simplifying Radicals and Complex Numbers Objectives • I can simplify Radicals to Lowest Terms • I can simplify negative radicals using “i” • I can simplify complex numbers using – Addition – Subtraction – Multiplication Symbols • Radical symbol Radical Index# Radicand Radical Basics • If there is no index number listed, it is assumed to be a 2 (Square Root) • The index number determines what root we are looking for Method for Simplifying • Prime Factor the number under the house (radical) • Look at the value of the index number • Cross off the index number of numbers or variables to bring one out of the house. • If you don’t have enough, then they stay under the house. Example 1 • Simplify: 36 2 2 33 2 2 33 23 6 • Factor the 36 36 2 18 2 9 3 3 Example 2 • Simplify: 12 • Factor the 12 12 2 23 2 23 2 3 2 6 2 3 Example 3 32 4 2 Example 3 20 2 5 Complex Numbers Real Numbers Rational Irrational Imaginary Numbers Complex Numbers The set of all numbers that can be written in the format: a + bi ; “a” is the real number part “bi’ is the imaginary part The Imaginary Unit i 1 where i 1 2 Example 4 20 2 5i Example 5 9 3i Example 6 48 4 3i Remember! i 1 2 Simplifying Complex Numbers • You can ONLY combine LIKE terms – Real parts – Imaginary parts a bi Real Imaginary (3 5i ) (7 8i) 10 3i 10 3i (4 7i) (1 4i) 5 11i 5 11i (6 2i) (9 3i) 3 5i 3 5i (8 7i ) (4 5i ) 4 12i 4 12i 3(5 7i ) 15 21i 15 21i 4(9 6i ) 36 24i 36 24i (3 4i )(9 2i) 27 6i 36i 8i 35 30i 2 i 1 2 (4 3i)(4 3i) 16 12i 12i 9i 25 2 i 1 2 Homework • WS 5-2 • Quiz next class