Complex Numbers MCQ for SLST Exam - Part 2

Complex Number – Part 2 (MCQ 21 to 40)

21. Which of the following is equal to i⁶?

a) i b) -1 c) -i d) 1

Correct Answer: b) -1
i⁶ = (i⁴)×(i²) = 1 × (-1) = -1

22. What is the conjugate of 5 - 2i?

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

Correct Answer: a) 5 + 2i
Change the sign of the imaginary part.

23. Which of the following is purely real?

a) 3i b) -4 c) 1 + 2i d) -i

Correct Answer: b) -4
Only real part is present.

24. The imaginary part of (4 + 7i) is:

a) 4 b) 7 c) 11 d) -7

Correct Answer: b) 7
Imaginary part = coefficient of i.

25. What is the polar form of 1 + i?

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

Correct Answer: a) √2(cos π/4 + i sin π/4)
r = √2, θ = tan⁻¹(1) = π/4

26. Let z = 2 - 5i, then |z| =

a) √29 b) √27 c) 7 d) 5

Correct Answer: a) √29
√(2² + (-5)²) = √(4 + 25) = √29

27. If z = 3 + 4i, then z̄ × z =

a) 5 b) 7 c) 25 d) 10

Correct Answer: c) 25
(3 + 4i)(3 - 4i) = 9 + 16 = 25

28. Which one represents the imaginary unit?

a) i b) 1 c) 0 d) -1

Correct Answer: a) i
Imaginary unit is defined as i = √(-1)

29. If z = a + ib, then |z|² =

a) a² - b² b) a² + b² c) a²b² d) ab

Correct Answer: b) a² + b²
|z|² = z × conjugate(z) = a² + b²

30. What is i⁰?

a) i b) 1 c) 0 d) -1

Correct Answer: b) 1
Any non-zero number to power 0 is 1

31. The value of (1+i)² is:

a) 2i b) 0 c) 2 d) i

Correct Answer: a) 2i
(1+i)² = 2i

32. Find the principal argument of -1 - i.

a) -π/4 b) -3π/4 c) π/4 d) 3π/4

Correct Answer: d) 3π/4
Argument in third quadrant.

33. Which of the following numbers is NOT imaginary?

a) 0 b) 2i c) -3i d) 7i

Correct Answer: a) 0
0 is neither real nor imaginary.

34. The reciprocal of i is:

a) i b) -i c) 1 d) -1

Correct Answer: b) -i
1/i = -i

35. What is the real part of 3 - 7i?

a) 7 b) -7 c) 3 d) -3

Correct Answer: c) 3
Real part = 3

36. The modulus of -3i is:

a) 3 b) -3 c) 0 d) 1

Correct Answer: a) 3
|-3i| = 3

37. If z₁ = 2+i and z₂ = 1-2i, then z₁+z₂ =

a) 1 - i b) 3 - i c) 3 + i d) 1 + i

Correct Answer: b) 3 - i
(2+i)+(1-2i)=3-i

38. The complex conjugate of -2+3i is:

a) 2-3i b) -2-3i c) 2+3i d) -2+3i

Correct Answer: b) -2-3i
Conjugate = change sign of imaginary part.

39. i³ equals:

a) i b) -i c) 1 d) -1

Correct Answer: b) -i
i³ = i² × i = (-1) × i = -i

40. The modulus of 1+i is:

a) √2 b) 1 c) 2 d) √3

Correct Answer: a) √2
|1+i| = √2