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CP Algebra II 11/12/15 Complex Numbers 1. Name: __________________ 4-4 Intro to Graph: f (x) = x 2 + 4x - 12 y-intercept: A.O.S.: Vertex: Domain: Range: 2. Graph: f (x) x 2 5 y-intercept: A.O.S.: Vertex: Domain: Range: 3. x-intercept(s): x-intercept(s): What are the solutions to the function f (x) x 2 5 , and how does the graph represent those solutions? 4. Support your conclusion from questions 2 and 3 by solving f (x) x 2 5 algebraically to find the xintercepts. There are solutions to f (x) x 2 5 that are not in the set of real numbers. Mathematicians developed imaginary numbers to solve such equations. Definition: Imaginary Unit: i 1 Definition: Complex Number: z a bi 5. Identify the real and imaginary parts given each complex number. a. z 3i 4 b. z=4 6. 2 3 4 5 Calculate the values of i ,i ,i , and i . 7. Evaluate. a. 8 i 14 b. c. i 78 z 8i 13 d. c. Perform the indicated operation for the complex numbers: a. (10 2i) (4 8i) b. (10 2i) (3 7i) i 308 z = -3i c. 9. (3 2i)(4 3i) d. 3i 2 3i Solve. a. x 2 16 b. 3x 2 12 0 Assignment: 1. Simplify: a. d. 121 i 13 b. i6 c. e. (2 3i) (4 5i) f. 72 2i(3 7i) 2. g. 5 2i 3 2i h. j. 5i 12 i 13 k. (2 7i)(3 4i) i. 3i 7 2i l. Solve. a. x 2 + 121 = 0 b. - 5x 2 - 50 = 0 96 (8 3i)(2 i)