Class 11 Mathematics Chapter 1 – Complex Numbers MCQs | FBISE | Grade 11 Math - MCQs

Practice 50 chapter-wise MCQs covering Complex Numbers for FBISE HSSC-I Mathematics.

1. A complex number is generally written in the form:

A) a + bi
B) a/b
C) ab + i
D) a − b

2. In z = a + bi, the real part of z is:

A) a
B) b
C) i
D) ab

3. In z = a + bi, the imaginary part of z is:

A) a
B) b
C) bi
D) i

4. The value of i² is:

A) 1
B) −1
C) i
D) −i

5. The value of i³ is:

A) 1
B) −1
C) i
D) −i

6. The value of i⁴ is:

A) 1
B) −1
C) i
D) −i

7. The conjugate of z = a + bi is:

A) a + bi
B) −a + bi
C) a − bi
D) −a − bi

8. The modulus of z = a + bi is:

A) a + b
B) √(a² + b²)
C) a² + b²
D) √(a² − b²)

9. The modulus of 3 + 4i is:

A) 3
B) 4
C) 5
D) 7

10. If z = 5 − 12i, then |z| equals:

A) 7
B) 13
C) 17
D) 144

11. Two complex numbers a + bi and c + di are equal if:

A) a = d and b = c
B) a = c and b = d
C) a + b = c + d
D) a − b = c − d

12. Which of the following is a purely real complex number?

A) 5 + 2i
B) 3i
C) −7
D) 2 − i

13. Which of the following is purely imaginary?

A) 4 + i
B) −6i
C) 6
D) 1 − 6i

14. The additive identity in the complex number system is:

A) 1
B) i
C) 0
D) −1

15. The multiplicative identity in the complex number system is:

A) 0
B) 1
C) i
D) −1

16. (3 + 2i) + (4 − 5i) equals:

A) 7 + 7i
B) 7 − 3i
C) −1 + 7i
D) −1 − 3i

17. (5 + 3i) − (2 + i) equals:

A) 3 + 2i
B) 7 + 4i
C) 3 + 4i
D) 7 + 2i

18. The product (2 + 3i)(4 − i) is:

A) 11 + 10i
B) 5 + 10i
C) 11 − 10i
D) 8 + 12i

19. The product (1 + i)(1 − i) is:

A) 0
B) 1
C) 2
D) 2i

20. The reciprocal of a non-zero complex number z is:

A) z
B) −z
C) 1/z
D) |z|

21. The reciprocal of 2 + 3i is:

A) (2 + 3i)/13
B) (2 − 3i)/13
C) (2 − 3i)/5
D) (3 − 2i)/13

22. To divide complex numbers, a useful method is to multiply numerator and denominator by the:

A) modulus
B) conjugate of the denominator
C) square of the numerator
D) imaginary unit only

23. For any complex number z, z z̄ is equal to:

A) z²
B) z + z̄
C) |z|²
D) 2z

24. If z = 3 + 4i, then z z̄ equals:

A) 5
B) 7
C) 25
D) 49

25. The real part of z + z̄ is:

A) 0
B) 2 Re(z)
C) 2 Im(z)
D) |z|

26. The expression z − z̄ is always:

A) real
B) purely imaginary
C) positive
D) equal to 1

27. The complex plane represents a complex number using:

A) only one axis
B) real and imaginary axes
C) two real axes only
D) a number line only

28. On the Argand plane, the horizontal axis is called the:

A) imaginary axis
B) real axis
C) modulus axis
D) conjugate axis

29. On the Argand plane, the vertical axis is called the:

A) real axis
B) modulus axis
C) imaginary axis
D) real-number axis

30. The point representing z = 3 + 4i on the Argand plane is:

A) (4, 3)
B) (3, 4)
C) (−3, 4)
D) (4, −3)

31. The argument of a non-zero complex number is the angle measured from the positive:

A) imaginary axis
B) real axis
C) negative imaginary axis
D) origin

32. If z lies on the positive real axis, its principal argument is:

A) π
B) π/2
C) 0
D) −π/2

33. If z lies on the positive imaginary axis, its principal argument is:

A) 0
B) π/2
C) π
D) 3π/2

34. The polar form of a complex number z is:

A) r(cos θ + i sin θ)
B) r(cos θ − sin θ)
C) r(sin θ + i cos θ)
D) r + θi

35. In the polar form z = r(cos θ + i sin θ), r represents the:

A) argument
B) modulus
C) imaginary part
D) real part only

36. In polar form, θ represents the:

A) modulus
B) real part
C) argument
D) conjugate

37. The polar form of 1 + i is:

A) √2(cos π/4 + i sin π/4)
B) 2(cos π/2 + i sin π/2)
C) √2(cos π/2 + i sin π/2)
D) cos π/4 + i sin π/4

38. The polar form of −1 + i has argument:

A) π/4
B) 3π/4
C) −π/4
D) π

39. De Moivre’s theorem is used for powers of complex numbers in:

A) Cartesian form only
B) polar form
C) logarithmic form only
D) matrix form

40. According to De Moivre’s theorem, [r(cos θ + i sin θ)]ⁿ equals:

A) r(cos nθ + i sin nθ)
B) rⁿ(cos nθ + i sin nθ)
C) nr(cos θ + i sin θ)
D) rⁿ(cos θ + i sin θ)

41. The value of (cos θ + i sin θ)² is:

A) cos θ + i sin θ
B) cos 2θ + i sin 2θ
C) cos²θ + i sin²θ
D) cos θ + i sin 2θ

42. The cube roots of unity are the roots of:

A) x² + 1 = 0
B) x³ − 1 = 0
C) x³ + 1 = 0
D) x² − 1 = 0

43. The three cube roots of unity are:

A) 1, i, −i
B) 1, ω, ω²
C) −1, i, −i
D) 0, 1, −1

44. If ω is a non-real cube root of unity, then:

A) 1 + ω + ω² = 1
B) 1 + ω + ω² = 0
C) 1 + ω = 0
D) ω + ω² = 1

45. For a non-real cube root of unity ω, the value of ω³ is:

A) 0
B) −1
C) 1
D) ω

46. The roots of z² + 1 = 0 are:

A) 1 and −1
B) i and −i
C) 0 and 1
D) 1 and i

47. If z = a + bi is purely real, then:

A) a = 0
B) b = 0
C) a = b
D) a = −b

48. If z = a + bi is purely imaginary, then:

A) a = 0
B) b = 0
C) a = b
D) a = 1

49. If |z| = 0, then z must be:

A) 1
B) i
C) 0
D) −1

50. If z is a non-zero complex number, then |z z̄| equals:

A) |z|
B) |z|²
C) 2|z|
D) 1/|z|

Explore More Class 11 Mathematics MCQs

Chapter 1 – Complex Numbers
Chapter 2 – Matrices and Determinants
Chapter 3 – Vectors
Chapter 4 – Sequences and Series
Chapter 5 – Polynomials
Chapter 6 – Permutation and Combination
Chapter 7 – Mathematical Induction and Binomial Theorem
Chapter 8 – Fundamentals of Trigonometry
Chapter 9 – Trigonometric Functions

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Syllabus & SLO Alignment

This chapter covers the fundamental concepts of complex numbers, including standard form, real and imaginary parts, conjugates, modulus, Argand plane, argument, polar form, De Moivre’s theorem, and roots of unity.

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