Complex Numbers MCQ for SLST Exam - Part 1

Complex Numbers MCQs for SLST Mathematics Exam

1. What is the value of (1 + i)(1 - i)?

a) 0 b) 1 c) 2 d) -1

Correct Answer: c) 2
(1 + i)(1 - i) = 1 - i² = 1 + 1 = 2

2. The modulus of 3 + 4i is:

a) 5 b) 7 c) 1 d) 4

Correct Answer: a) 5
√(3² + 4²) = √(9 + 16) = √25 = 5

3. The conjugate of a complex number a + ib is:

a) a - ib b) a + ib c) -a + ib d) -a - ib

Correct Answer: a) a - ib
Conjugate reverses the sign of imaginary part.

4. What is i⁴ equal to?

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

Correct Answer: c) 1
(i²)² = (-1)² = 1

5. Principal argument of (1+i) is:

a) π/4 b) π/2 c) π/3 d) π/6

Correct Answer: a) π/4
Arg(1+i) = tan⁻¹(1/1) = π/4

6. (2+3i) + (4+5i) equals:

a) 6+8i b) 2+15i c) 8+2i d) 6+2i

Correct Answer: a) 6+8i
Add real and imaginary parts separately.

7. Multiplicative inverse of i is:

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

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

8. Modulus of 0 is:

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

Correct Answer: a) 0
Modulus of 0 is 0.

9. Square of i is:

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

Correct Answer: b) -1
i² = -1

10. (1+i)³ equals:

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

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

11. Which number is purely imaginary?

a) 5 b) 2+i c) i d) 3-4i

Correct Answer: c) i
Only imaginary part non-zero.

12. What is the value of |1-i|?

a) 1 b) √2 c) 2 d) 0

Correct Answer: b) √2
√(1² + (-1)²) = √2

13. i raised to power 5 is:

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

Correct Answer: a) i
i⁵ = i⁴ × i = 1 × i = i

14. What is (2-i)(3+i)?

a) 5+i b) 5-i c) 7+i d) 7-i

Correct Answer: a) 5+i
(2×3 + 2×i + -i×3 + (-i²)) = (6 + 2i - 3i +1) = 7 - i

15. If z = 2+3i, then |z|² is:

a) 13 b) 12 c) 5 d) 9

Correct Answer: a) 13
(2)² + (3)² = 4 + 9 = 13

16. Real part of i² is:

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

Correct Answer: b) -1
i² = -1, real part = -1

17. Imaginary part of 5-7i is:

a) 5 b) -7 c) 7 d) -5

Correct Answer: b) -7
Imaginary part = -7

18. 1/(1+i) equals:

a) 1+i b) (1-i)/2 c) (1+i)/2 d) (1-i)

Correct Answer: b) (1-i)/2
Rationalizing denominator

19. Argument of -1-i is:

a) -3π/4 b) 3π/4 c) π/2 d) -π/2

Correct Answer: b) 3π/4
-1 and -1 both negative => 3π/4

20. Which of the following is not a complex number?

a) 0 b) 2 c) i d) None of these

Correct Answer: d) None of these
All are complex numbers