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PM 5000 Un acercamiento a la ingeniería Agosto-diciembre 2016 Prepa Tec Campus Aguascalientes Actividad 6 Números Complejos I Nombre_____________________________Matrícula_____________ Número de lista_______ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may apply. 1) 12 - 5i 1) A) complex, pure imaginary B) real, complex C) none of these D) complex, nonreal complex 2) 13 3) 2) A) complex, nonreal complex C) real, complex B) pure imaginary D) complex, pure imaginary 9i A) complex, pure imaginary C) real, complex B) real D) complex, nonreal complex 3) Write the number as the product of a real number and i. 4) -25 A) -i 25 B) 5 i 5) - -121 A) 11 6) - -175 A) 5i 7 4) 5) B) i 121 C) 11i 9) 10) D) -11i 6) B) -5 7i Perform the indicated operations. Simplify the answer. 7) -3 ∙ -3 A) 3 B) 3i 8) D) -5i C) 5i C) 5 7i D) -5i 7 C) -3i D) -3 7) -125 ∙ -5 A) 5 B) -25 C) 25i D) 5i -3 ∙ -5 A) - 15i B) 15 C) - 15 D) 15i 8) 9) -33 -3 A) 11 10) B) 11i C) 1 11 D) i 11 11) -8 128 A) - 11) i 4 B) i 4 C) 1 4 D) - 1 4 Write the number in standard form a + bi. -4 - -20 12) 2 A) -2 + i 5 13) 12) B) -2 - i 5 C) -2 - i 10 D) -2 + i 10 6 + -63 3 A) 2 - i 7 13) B) 2 + i 7 C) 2 - i 21 Perform the indicated operation. Write the result in standard form. 14) (3 - 7i) + (9 + 5i) A) -12 + 2i B) 12 - 2i C) 12 + 2i 15) (-5 - 7i) + (10 + 4i) A) 10 - 3i 16) (-4 - 5i) - (7 - i) A) -11 + 4i D) 2 + i 21 14) D) -6 + 12i 15) C) 10 + 3i B) 5 + 3i D) 5 - 3i 16) C) -11 - 5i D) 11 + 4i 17) (9 + 7i) - (-4 + 3i) + (-1 - 7i) A) 12 + 3i B) 4 + 3i C) 12 - 3i D) -12 + 11i Find the product. Write the answer in standard form. 18) 2i(8 - 7i) A) - 16i - 14i2 B) 14 + 16i C) 16i - 14 D) 16i + 14i2 C) -63i2 + 9i - 54 D) -9 - 117i 19) (9 - 9i)(6 + 7i) A) 117 + 9i B) -11 - 4i 17) 18) 19) B) 117 - 9i 20) 3i(3 + 6i)2 20) A) -108i + 108i2 + 108i3 B) -81i C) -81 + 108i D) -108 - 81i 21) ( 13 - 7i)( 13 + 7i) A) 13 - 49i 22) (5 + i)(5 - i)(2 - 3i) A) 48 - 72i 21) B) 20 C) 62 D) 13 + 49i 22) B) 52 - 78i C) 22 - 98i 2 D) 18 - 92i Simplify the power of i. 23) i96 A) 1 24) i49 A) i 25) B) -i C) i D) -1 B) 1 C) -1 D) -i 24) 1 27 i 25) A) 1 26) 23) C) -i B) i D) -1 1 -8 i 26) A) 1 B) -i C) -1 D) i Find the quotient. Write the answer in standard form. 8 + 3i 27) 6 - 9i 5 2 A) - + i 3 3 28) 1 17 - i 25 25 C) - 7 2 + i 45 3 D) 7 10 + i 39 13 28) B) - 17 i 25 C) - 19 17 - i 25 25 D) 19 17 - i 25 25 -10 -i 29) A) -10i 30) 25 18 + i 13 13 5 - i -3 + 4i A) 29) B) 27) B) -10 C) 10i D) 10 6 - 9i 6 + 2i A) 30) 9 33 + i 32 32 B) 27 33 + i 16 32 C) 9 33 - i 20 20 D) 27 21 + i 10 10 In work with alternating current, complex numbers are used to describe current I, voltage E, and impedance Z. These three quantities are related by the equation E = IZ. Solve the equation E = IZ for the missing variable. 31) 31) I = 7 + 2i, Z = 5 + 4i B) E = 35 + 8i C) E = 43 + 38i D) E = 27 + 38i A) E = 35 + 46i 3