Complex Numbers Assessment Solutions PDF

## Mr. Answer Key **55 Points** The scariest costume I saw on Halloween was someone dressed up as Mr. Gelada. **NO GRAPHING CALCULATORS** Hon Alg 2 Complex Numbers Assessment **1. use K = -5i + 4 V = -3 - 6i to answer the following with answers in a+bi form and simplified.** a. 2K - 5V **4pts** -1...

## Mr. Answer Key **55 Points** The scariest costume I saw on Halloween was someone dressed up as Mr. Gelada. **NO GRAPHING CALCULATORS** Hon Alg 2 Complex Numbers Assessment **1. use K = -5i + 4 V = -3 - 6i to answer the following with answers in a+bi form and simplified.** a. 2K - 5V **4pts** -10i + 8 ____ (-15 - 30i) 2.3 + 20i -10i + 8 + 15 + 30i b. (-2V)(K) **4pts** (6 + 12i)(-5i + 4) -30i + 24 - 60i² + 48i 84 + 18i c. V/K **5pts** -3 - 6i ____ 4 - 5i -12 - 15i - 24i + 30 ____ 4 + 5i 16 + 25 18 - 39i ____ 41 d. Product of V and its complex conjugate **4pts** (-3 - 6i)(-3 + 6i) 9 - 18i + 18i + 36 = 45 e. H(x) is a quadratic function with V as one of its zeros. It passes though the point (-3, -144). Find H(x) and write it as a functional equation in standard form. **6pts** (x + 3 + 6i)(x + 3 - 6i) x² + 3x - 6ix + 3x + 6ix + 9 - 18i + 36 + 18i H(x) = a(x² + 6x + 45) -144 = a(9 - 18 + 45) -144 = 36a a = -144 ____ 36 H(x) = -4x² - 24x - 180 ## 2. Show two different ways to determine if -10-2i is a zero of the function: g(x) = x² + 20x + 104 **6pts** a) g(-10-2i) = 0? (-10-2i)² + 20(-10 - 2i) + 104 = 0 100 + 40i - 4 - 200 - 40i + 104 = 0 **yes!** b) (x + 10 + 2i)(x + 10 - 2i) x² + 10x - 2ix + 10x + 100 - 20i + 2ix + 20i + 104 x² + 20x + 104 **yes!** c) quad formula x = -b ± √b² - 4ac ____ 2a -20 ± √400 - 4 * 1 * 104 ____ 2 -20 ± √-16 ____ 2 -20 ± 4i ____ 2 -10 ± 2i **yes!** ## 3. m(x) is a parent function (not constant or linear) with 5 transformations that is neither even nor odd. Find a possible example for m(x) then show that is it neither using functional notation. **4pts** m(x) = 2(- (x/3)²) - 7 m(-x) - 2(- (-x/3)²) - 7 -m(x) = (-2(- (x/3)²) - 7) = 2(x/3)² + 7 m(x) ≠ m(-x) not even m(-x) ≠ -m(x) not odd ## 4. (√-45 + √-20)x√-36 - √-49) Rewrite in a + bi form. Simplify if possible. {6pts} √-16 + 3√27 (3i√5 + 2i√5)(6i - 7i) 4i - 3i (5i√5)(-i)(-3 - 4i) -3 + 4i 5√5 - 3 - 4i = - 15√5 - 20i√5 i -3 + 4i - 3 - 4i 9 + 16 = 25 -3√5 ____ 5 - 4i√5 ____ 5 ## 5. Find the difference quotient for the function g(x) = -3x² + 8x - 7 {4pts} g(x + h) - g(x) ____ h -3(x² + 2xh + h²) + 8(x + h) - 7 - (-3x² + 8x - 7) ____ h -3x² - 6xh - 3h² + 8x + 8h - 7 + 3x² - 8x + 7 ____ h -6xh - 3h² + 8h ____ h -6x - 3h + 8 ## 6. P(x) is a 6th degree polynomial function with real number coefficients. Several of its zeros are 5, 7i, -11, 6i + 9. {6pts} a. Write all the factors of P(x) b. how many x-intercepts does P(x) have? a. P(x) = (x - 5)(x + 11)(x - 7i)(x + 7i)(x - 9 - 6i)(x - 9 + 6i) b. 2 real zeros so 2 x-intercepts ## 7. Draw an example of a quadratic function with no x-intercepts that is also an even function. Write the function and find the non-real zeros of the function you chose. 6pts f(x) = x² + 4 0 = x² + 4 -4 = x² ±√-4 = x ±2i = x ## 8. f(x) = -7 - 5 (-x + 11)² / 7 **parent 5x** Transformation functional notation new function (left 11) f(x + 11) x + 11 Horiz stretch 1/2 f(2x) 5 (2x + 11) Ref y f(-x) - 5 (2x + 11) Ref x -f(x) - 5 (2x + 11) down 7 f(x) - 7 - 5 (2x + 11) - 7 ## 9. f(x) = √x + 9 D: [-9, ∞) g(x) = 1 / (x - 16) x ≠ ±4 a. find the domain of (f + g)(x) b. find the domain of (g / f)(x) c. find the domain of g(f(x)) E (-9, -4) U (-4, 4) U (4, ∞) (-9, -4) U (-4, 4) U (4, ∞) (√x + 9) - 16 = x + 9 - 16 = x - 7 x ≠ 7 E (-9, 7) U (7, ∞) ## 10. find 8/5 ÷ i = 8/5 * i = 8i/5