AP ECET MATHEMATICS Multiple Choice Questions (MCQs)

46. What is the modulus of the complex number 3 + 4i?

• a) 5
• b) 7
• c) 1
• d) 4

Answer: a) 5

47. The conjugate of the complex number 2 + 5i is:

• a) 2 - 5i
• b) -2 + 5i
• c) -2 - 5i
• d) 5 - 2i

Answer: a) 2 - 5i

48. Which of the following is the modulus of the complex number -3 - 4i?

• a) 7
• b) 5
• c) 6
• d) 1

Answer: a) 7

49. The product of two complex numbers (3 + 2i) and (1 - 4i) is:

• a) 11 - 10i
• b) 7 - 10i
• c) 11 + 10i
• d) 7 + 10i

Answer: b) 7 - 10i

50. In the polar form, the modulus of the complex number z = 1 + i is:

• a) √2
• b) 1
• c) 2
• d) 3

Answer: a) √2

51. What is the argument of the complex number 1 + √3i?

• a) π/6
• b) π/3
• c) π/4
• d) π/2

Answer: b) π/3

52. The polar form of the complex number 1 - i is:

• a) √2(cos(−π/4) + i sin(−π/4))
• b) √2(cos(π/4) + i sin(π/4))
• c) √2(cos(−π/2) + i sin(−π/2))
• d) 1 + i

Answer: a) √2(cos(−π/4) + i sin(−π/4))

53. Euler’s formula for complex numbers is given by:

• a) e^(ix) = cos(x) + i sin(x)
• b) e^(ix) = cos(x) - i sin(x)
• c) e^(ix) = cos(x) - i
• d) e^(ix) = cos(x) + i

Answer: a) e^(ix) = cos(x) + i sin(x)

54. What is the value of (1 + i)^2?

• a) 1 - 2i
• b) -1 + 2i
• c) 2 + 2i
• d) 1 + 2i

Answer: b) -1 + 2i

55. De Moivre's Theorem states that:

• a) (cos(θ) + i sin(θ))^n = cos(nθ) + i sin(nθ)
• b) (cos(θ) + i sin(θ))^n = cos(θ) + i sin(nθ)
• c) (cos(θ) + i sin(θ))^n = cos(nθ) - i sin(nθ)
• d) (cos(θ) - i sin(θ))^n = cos(nθ) + i sin(nθ)

Answer: a) (cos(θ) + i sin(θ))^n = cos(nθ) + i sin(nθ)

56. Which of the following is the polar form of the complex number 3 + 4i?

• a) 5(cos(53.13°) + i sin(53.13°))
• b) 5(cos(45°) + i sin(45°))
• c) 4(cos(53.13°) + i sin(53.13°))
• d) 3(cos(53.13°) + i sin(53.13°))

Answer: a) 5(cos(53.13°) + i sin(53.13°))

57. If z = 3 + 4i, what is the value of z^2?

• a) 1 + 2i
• b) -7 + 24i
• c) 7 + 24i
• d) -7 - 24i

Answer: b) -7 + 24i

58. The polar form of the complex number -2 + 2i is:

• a) 2√2(cos(135°) + i sin(135°))
• b) 2√2(cos(45°) + i sin(45°))
• c) 2(cos(135°) + i sin(135°))
• d) 2√2(cos(225°) + i sin(225°))

Answer: a) 2√2(cos(135°) + i sin(135°))

59. The sum of the complex numbers (4 + 3i) and (2 - 5i) is:

• a) 6 - 2i
• b) 6 + 2i
• c) 2 - 8i
• d) 6 + 8i

Answer: b) 6 + 2i

60. Which of the following is an application of De Moivre’s Theorem?

• a) Finding square roots of complex numbers
• b) Multiplying complex numbers
• c) Dividing complex numbers
• d) All of the above

Answer: d) All of the above