Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Over Lesson 5–3 Solve x 2 – x = 2 by factoring. A. 2, –1 B. 1, 2 0% A B C 0% D D A 0% B D. –1, 1 C C. 1, 1 A. B. C. 0% D. Over Lesson 5–3 Solve c 2 – 16c + 64 = 0 by factoring. A. 2 B. 4 0% A B C 0% D D A 0% B D. 12 C C. 8 A. B. C. 0% D. Over Lesson 5–3 Solve z 2 = 16z by factoring. A. 1, 4 B. 0, 16 0% A B C 0% D D A 0% B D. –16 C C. –1, 4 A. B. C. 0% D. Over Lesson 5–3 Solve 2x 2 + 5x + 3 = 0 by factoring. A. A 0% 0% B D. A B C 0% D D C. –1 A. B. C. 0% D. C B. 0 Over Lesson 5–3 Write a quadratic equation with the roots –1 and 6 in the form ax 2 + bx + c, where a, b, and c are integers. A. x2 – x + 6 = 0 0% B D. x2 – 6x + 1 = 0 A 0% A B C 0% D D C. x2 – 5x – 6 = 0 C B. x2 + x + 6 = 0 A. B. C. 0% D. • imaginary unit • pure imaginary number • complex number • complex conjugates Definitions The imaginary unit is The imaginary number is i2 1 i For any positive real numbers b -b 2 b 2 1 ib 1 Square Roots of Negative Numbers A. Answer: A. A. B. 0% B A 0% A B C 0% D D D. C C. A. B. C. 0% D. Square Roots of Negative Numbers B. Answer: B. A. B. 0% B A 0% A B C 0% D D D. C C. A. B. C. 0% D. Products of Pure Imaginary Numbers A. Simplify –3i ● 2i. –3i ● 2i = –6i 2 = –6(–1) =6 Answer: 6 i 2 = –1 A. Simplify 3i 5i. A. 15 B. –15 0% B A 0% A B C 0% D D D. –8 C C. 15i A. B. C. 0% D. Products of Pure Imaginary Numbers B. 1 4 1 2 2 Answer: 6 6 6 B. Simplify . A. B. 0% B A 0% A B C 0% D D D. A. B. C. 0% D. C C. Equation with Pure Imaginary Solutions Solve 5y 2 + 20 = 0. 5y 2 + 20 = 0 5y 2 = –20 y 2 = –4 Original equation Subtract 20 from each side. Divide each side by 5. Take the square root of each side. Answer: y = 2i Solve 2x 2 + 50 = 0. C. 5 D. 25 0% 0% A. B. C. 0% D. A B C 0% D D 25i C B. B 5i A A. Equate Complex Numbers Find the values of x and y that make the equation 2x + yi = –14 – 3i true. Set the real parts equal to each other and the imaginary parts equal to each other. 2x = –14 Real parts x = –7 Divide each side by 2. y = –3 Imaginary parts Answer: x = –7, y = –3 Find the values of x and y that make the equation 3x – yi = 15 + 2i true. A. x = 15 y=2 0% B 0% A D. x = 5 y = –2 A B C 0% D D C. x = 15 y = –2 A. B. C. 0% D. C B. x = 5 y=2 Add and Subtract Complex Numbers A. Simplify (3 + 5i) + (2 – 4i). (3 + 5i) + (2 – 4i) = (3 + 2) + (5 – 4)i =5+i Answer: 5 + i Commutative and Associative Properties Simplify. A. Simplify (2 + 6i) + (3 + 4i). A. –1 + 2i B. 8 + 7i 0% B A 0% A B C 0% D D D. 5 + 10i C C. 6 + 12i A. B. C. 0% D. Add and Subtract Complex Numbers B. Simplify (4 – 6i) – (3 – 7i). (4 – 6i) – (3 – 7i) = (4 – 3) + (–6 + 7)i Commutative and Associative Properties =1+i Answer: 1 + i Simplify. B. Simplify (3 + 2i) – (–2 + 5i). A. 1 + 7i B. 5 – 3i 0% B A 0% A B C 0% D D D. 1 – 3i C C. 5 + 8i A. B. C. 0% D. Multiply Complex Numbers (1 + 4i)(3 – 6i) = 1(3) + 1(–6i) + 4i(3) + 4i(–6i) FOIL = 3 – 6i + 12i – 24i 2 Multiply. = 3 + 6i – 24(–1) i 2 = –1 = 27 + 6i Add. Answer: 27 + 6i (1 – 3i)(3 + 2i) A. 4 – i B. 9 – 7i C. –2 – 5i D. 9 – i A. B. C. D. A B C D Divide Complex Numbers A. 3 – 2i and 3 + 2i are conjugates. Multiply. i2 = –1 a + bi form Answer: A. A. B. 3 + 3i 0% A B C 0% D D A 0% B D. C C. 1 + i A. B. C. 0% D. Divide Complex Numbers B. Multiply by Multiply. i2 = –1 a + bi form Answer: . B. A. A 0% 0% B D. A B C 0% D D C. A. B. C. 0% D. C B.