Name: A2 HW Imaginary Numbers Rewrite the following in terms of i and in simplest form: 1) 100 2) 289 3) 15 4) 4 81 5) 5 12 6) -8 72 Rewrite the following as a radical: 7) 12i 8) 20i Solve for x in simplest radical form: 9) x 2 + 16 = 0 10) 4x 2 + 80 = 0
Simplify the following powers of i: 11) i 57 12) 2i 88 13) -5i 66 14) 7i 127 15) What is the value of (5i 3 ) 3? (1) -125i (3) 15i (2) 125i (4) 15i 16) Given the quadratic 3x 2 2x = 4, which of the following best describes its roots? (1) two unequal, non-real roots (2) two real, unequal, irrational roots (3) two real, equal, rational roots (4) two real, unequal, rational roots 17) Find the solution set to: 4x + 2 + 3 11
Name: A2 HW Ops w/ Imag Numbers 1) Rewrite the following in terms of i and in simplest form: a. 16 b. 72 c. 4 242 2) Perform the indicated operations and simplify: a. 8i i b. (9i)(8i) c. 2 9 + 49 d. 16 4 e. 25 + 25 f. 6 3 3) When expressed as a monomial in terms of i, 2 32 5 8 is equivalent to (1) 2 2 i (2) 2i 2 (3) -2i 2 (4) 18i 2
4) Multiply and simplify your answer: ( 2 )(6 75 ) 5) Solve for x in simplest radical form: 5x 2 + 225= 0 6) The expression i 100 + i 101 + i 102 equals (1) 1 (3) -i (2) -1 (4) i 7) If f(x) = 4x 22 + 7x 56 x 33, find f(i). 8) Solve for x using any appropriate method: x 2 + 6x 1 = 0
Name: A2 HW Complex Numbers Perform the indicated operation and express your answer in simplest a + bi form: 1) (-6 + 5i) + (6 i) 2) (-1 + 8i) (-5 2i) 3) (6 + 49 ) + (3 + 64 ) 4) (-1 + 2 12 ) (8 + 5 48 ) Find values for a and b that will make each statement true: 5) (a + bi) + (4 + 6i) = 9 + 11i 6) (10 + 3i) (a + bi) = 7 6i 7) When simplified, 4 12 5 48 is equal to (1) 28i 3 (2) 4i 3 (3) 12i 3 (4) 32i 3 8) Which of the following is not equal to the other three? (1) i 19 (2) i 9 (3) i 27 (4) i 35 9) When 6i 18 is multiplied by 8i 6 the product is (1) 48i (2) 48i (3) 48 (4) 48
10) If f(x) = 1 2 x +, then f -1 5 5 (x) is equal to which of the following: (1) 5x + 2 (2) 5x 2 (3) 1 2 x 2 (4) 5x - 5 5 5 11) Graph the following complex numbers and label: C (4 + 3i) O (-5 + 4i) M (2 9i) P (-8 3i) L 4 E -6i X (7i 1) 12) If a = -3 + 2i and b = 4 i, in which quadrant does the graph of a b lie? 13) On the grid below, graph the sum of (2 + 49 ) and (-3-25 ).
Name A2 HW Multiplying Complex Numbers 1) (2 3i) (7 + 2i) 2) (4i + 8) (4i 8) 3) (5 4)(2 + 36) 4) (3 7i) 2 5) (4-2i 3)(5 + i 3) 6) 2(3 9i) 2i 2 7) Give the following in terms of 1, i, -1, -I: a. i 57 b. 2i 88
8) Simplify: 1 96 4 9) Simplify into a + bi Form: 2i 13 i 87 + 4i 40 10) Subtract 2 180 from 45. (11) Simplify: 1 + 4 x 1 3 + 2 x 9 x 2 12) Find the roots of the quadratic equation by completing the square: 3x 2 12x 21 = 0
Name A2 HW Imag/ Complex Number Review In 1-4, true or false: 1) The solutions to x 2 = -5 are 5 and 5. 2) The solutions to g 2 = -13 are 13i and 13i. 3) i 31 = i 31. 4) i 17 is a square root of 17. In 5-7, express each number in terms of i, and simplify: 5) 2 49 6) 28 7) 10 In 8 9, write each given power in simplest terms as 1, i, -1, or I: 8) i 72 9) 4i 91 In 10-14, write each number in terms of i, perform the indicated operation, and write the answer in simplest terms. 10) 3 4 + 121 11) 8 3 12 12) 5 80
13) 4 48 3 14) 3i(4i + 5i) In 15-18, perform the indicated operation and express the result in simplest a + bi form: 15) (6 i) + (3 + 4i) 16) (-3 i) (1 + 4i) 17) (4 + 2i)(-3 i) 18) ( 3 27)(6 + 75) 19) Solve the given expression using the quadratic formula: 3x 2 = 4x + 1 20) Solve the system algebraically and check: 2 y = x 2x 15 x + y = 3
Name A2 HW Rationalizing w/ Imag Numbers Rationalize the expression and write your answer in simplest a +bi form: 3 9 3i 1) 2) 2 + i 6i 3) 5 + 8i 3 i 4) 7 + 4i 7 4i 5) What is the difference when 5 6i is subtracted from 4+7i? Multiply and write your answer in simplest a + bi form. 6) (4-25)(1 + 81) 7) 6(2 i) 6i 2
8) (3-8 ) (1-18 ) 9) What is the sum of 8i 26 +4i 60 10) If f(x) = -x 2 + 5x, find f(-3). 11) Given the equation: x 2 + y 2 4x + 6y 3 = 0 a) Find the center-radius form of this equation. b) Determine the center and radius of the circle.
Name A2 HW - Solving with Imaginary Roots Solve the following equations and express your answers in simplest a + bi form: 1) x 2 6x + 25 = 0 2) x 2 = x 5 2 3) 3x 2 = 6(x 1)
Perform the operations and express your answers in simplest a + bi form: 4) 6 3 + 4i 5i 5) (2-27 ) + (-7 + 5 12 ) 6) (7 2i)(1 4i) 7) (5 18 )(3 32 ) 8) Express the following in simplest a + bi form: 3i 39 + i 76 10i 226 9) If y = -5x 2 is translated 17 units down and 8 units to the right, what would the new equation be? 10) Written in simplest form, 3 2 3x 27xy 2 12x + 36xy is equivalent to (1) x + 3y 4 (2) x + 4y 3 (3) x 3y 4 (4) x 3y 4(x + 3y)
Name A2 HW The Discriminant (Day 2) For each of the following, determine whether the roots are: (1) real, rational, and equal (2) real, rational, and unequal (3) real, irrational, and unequal (4) imaginary 1) 2x 2 + 7x 15 = 0 2) x 2 + 2 = 9x 3) 5x 2 = x - 3 4) 4x 2 + 9 = 12x 5) When expressed as a monomial in terms of i, 2 32 5 8 is equivalent to (1) 2 2i (2) 2 i 2 (3) 2i 2 (4) 18 i 2 6) Solve for x in simplest a + bi form: 3x 2 + 10 = 4x 7) Rationalize the following and express your answer in simplest a + bi form: a. 4 +7i 8i b. 7 + 3i 4 2i
8) Graph the following complex numbers and their sum: (-3 2i) +(-1 + 4i) 9) Which is a true statement about the graph of the equation y = x 2 7x 60? (1) It is tangent to the x-axis (2) It does not intersect the x-axis. (3) It intersects the x-axis in two distinct points that have irrational coordinates. (4) It intersects the x-axis in two distinct points that have rational coordinates 10) Which of the following would be the discriminant of a parabola that crosses the x-axis at irrational coordinates? (1) -11 (2) 0 (3) 36 (4) 143 11) For what integer value of a would ax 2 6x + 8 = 0 produce non-real roots? (1) 1 (2) 2 (3) 0 (4) -1 12) For what value of b will the roots of 2x 2 bx + 9 = 0 produce two real, unequal, irrational roots. (1) -1 (2) 0 (3) 5 (4) 10
Name A2 HW Sum and Product of the Roots 1) For the quadratic equation 2x 2 + 14x + 6 = -2, find: a) the sum of the roots b) the product of the roots 2) If the roots of the equation x 2 4x + c = 0 are 2 + 3i and 2 3i, what is the value of c? 3) If one roots of a quadratic equation is 5 + 7i, what is the other root and the equation? 4) If one roots of x 2 6x + k = 0 is 4, find the other root. 5) Find the sum of the roots and subtract it from the product of the roots of the equation: 4x 2 16x + 20 = 0
6) Which equation has the complex number 4 3i as a root? (1) x 2 + 6x 25 = 0 (3) x 2 + 8x 25 = 0 (2) x 2 6x + 25 = 0 (4) x 2 8x + 25 = 0 7) Which number could represent the discriminant of a quadratic equation whose roots are real, unequal, and irrational? (1) 0 (2) -5 (3) 7 (4) 4 8) Which of the following has real, rational, and equal roots? (1) 9x 2 + 6x + 1 = 0 (3) 4x 2 9 = 0 (2) 2x 2 + 7x 10 = 0 (4) x 2 + 9 = 0 9) The roots of x 2 16x + 61 = 0 are (1) real, rational, and equal (3) real, irrational, and unequal (2) real, rational, and unequal (4) imaginary 10) In which quadrant do the following vectors lie? a. 3 2i b. -5 + 7i c. -2-6i 11) If a parabola touches the x-axis only once, what is the value of the discriminant?