VIVA / INTERVIEW QUESTIONS WITH ANSWERS
CHAPTER: COMPLEX NUMBERS
1. What is a complex number? √
Answer: A number of the form a + ib, where a and b are real numbers and i = −1.
2. What is the value
√ of i?
Answer: i = −1.
3. What is i2 ?
Answer: i2 = −1.
4. What is the real part of a complex number?
Answer: The real part is the number without i. For z = a + ib, real part is a.
5. What is the imaginary part of a complex number?
Answer: The imaginary part is the coefficient of i. For z = a + ib, imaginary part is b.
6. Is 0 a complex number?
Answer: Yes, because 0 = 0 + i0.
7. Is every real number a complex number?
Answer: Yes, every real number can be written as a + i0.
8. Is i a real number?
Answer: No, i is an imaginary number.
9. What is i3 ?
Answer: i3 = −i.
10. What is i4 ?
Answer: i4 = 1.
11. What is the cycle of powers of i?
Answer: i, −1, −i, 1 (repeats every 4).
12. When are two complex numbers equal?
Answer: When their real parts and imaginary parts are equal.
13. How do you add two complex numbers?
Answer: Add real parts and imaginary parts separately.
,14. How do you subtract two complex numbers?
Answer: Subtract real parts and imaginary parts separately.
15. How do you multiply complex numbers?
Answer: Multiply normally using distributive law and replace i2 by −1.
16. How do you divide complex numbers?
Answer: Multiply numerator and denominator by the conjugate of the denominator.
17. What is the conjugate of a complex number?
Answer: The conjugate of a + ib is a − ib.
18. What is the product of a complex number and its conjugate?
Answer: It is always a real number.
19. Why do we use conjugates?
Answer: To remove i from the denominator.
20. What is the modulus of a complex number?
Answer: The distance of the complex number from origin in the complex plane.
21. Write the formula for modulus.
Answer: √
|a + ib| = a2 + b 2
22. Is modulus always positive?
Answer: Yes, modulus is always non-negative.
23. What is |z|2 equal to?
Answer: |z|2 = zz̄.
24. What is the argument of a complex number?
Answer: The angle made by the complex number with the positive x-axis.
25. What is principal argument?
Answer: The argument lying between −π and π.
26. Can a complex number have more than one argument?
Answer: Yes, it has infinitely many arguments.
27. What is the complex plane?
Answer: A plane where x-axis represents real part and y-axis represents imaginary part.
28. What is the position of a purely imaginary number?
Answer: On the y-axis.
, 29. What is the position of a purely real number?
Answer: On the x-axis.
30. What is polar form of a complex number?
Answer: z = r(cos θ + i sin θ).
31. What is r in polar form?
Answer: r is the modulus of the complex number.
32. What is θ in polar form?
Answer: θ is the argument of the complex number.
33. State De Moivre’s theorem.
Answer:
(cos θ + i sin θ)n = cos nθ + i sin nθ
34. When is De Moivre’s theorem used?
Answer: To find powers and roots of complex numbers.
35. How many nth roots does a complex number have?
Answer: Exactly n distinct roots.
36. How are roots placed in complex plane?
Answer: They are equally spaced on a circle.
37. Is addition of complex numbers commutative?
Answer: Yes.
38. Is multiplication of complex numbers associative?
Answer: Yes.
39. Does zero have a multiplicative inverse?
Answer: No.
40. Why are complex numbers important?
Answer: They help in solving equations which have no real solutions.
41. Give one real-life use of complex numbers.
Answer: Used in electrical engineering and signal processing.
42. Can we compare complex numbers?
Answer: No, complex numbers cannot be compared like real numbers.
CHAPTER: COMPLEX NUMBERS
1. What is a complex number? √
Answer: A number of the form a + ib, where a and b are real numbers and i = −1.
2. What is the value
√ of i?
Answer: i = −1.
3. What is i2 ?
Answer: i2 = −1.
4. What is the real part of a complex number?
Answer: The real part is the number without i. For z = a + ib, real part is a.
5. What is the imaginary part of a complex number?
Answer: The imaginary part is the coefficient of i. For z = a + ib, imaginary part is b.
6. Is 0 a complex number?
Answer: Yes, because 0 = 0 + i0.
7. Is every real number a complex number?
Answer: Yes, every real number can be written as a + i0.
8. Is i a real number?
Answer: No, i is an imaginary number.
9. What is i3 ?
Answer: i3 = −i.
10. What is i4 ?
Answer: i4 = 1.
11. What is the cycle of powers of i?
Answer: i, −1, −i, 1 (repeats every 4).
12. When are two complex numbers equal?
Answer: When their real parts and imaginary parts are equal.
13. How do you add two complex numbers?
Answer: Add real parts and imaginary parts separately.
,14. How do you subtract two complex numbers?
Answer: Subtract real parts and imaginary parts separately.
15. How do you multiply complex numbers?
Answer: Multiply normally using distributive law and replace i2 by −1.
16. How do you divide complex numbers?
Answer: Multiply numerator and denominator by the conjugate of the denominator.
17. What is the conjugate of a complex number?
Answer: The conjugate of a + ib is a − ib.
18. What is the product of a complex number and its conjugate?
Answer: It is always a real number.
19. Why do we use conjugates?
Answer: To remove i from the denominator.
20. What is the modulus of a complex number?
Answer: The distance of the complex number from origin in the complex plane.
21. Write the formula for modulus.
Answer: √
|a + ib| = a2 + b 2
22. Is modulus always positive?
Answer: Yes, modulus is always non-negative.
23. What is |z|2 equal to?
Answer: |z|2 = zz̄.
24. What is the argument of a complex number?
Answer: The angle made by the complex number with the positive x-axis.
25. What is principal argument?
Answer: The argument lying between −π and π.
26. Can a complex number have more than one argument?
Answer: Yes, it has infinitely many arguments.
27. What is the complex plane?
Answer: A plane where x-axis represents real part and y-axis represents imaginary part.
28. What is the position of a purely imaginary number?
Answer: On the y-axis.
, 29. What is the position of a purely real number?
Answer: On the x-axis.
30. What is polar form of a complex number?
Answer: z = r(cos θ + i sin θ).
31. What is r in polar form?
Answer: r is the modulus of the complex number.
32. What is θ in polar form?
Answer: θ is the argument of the complex number.
33. State De Moivre’s theorem.
Answer:
(cos θ + i sin θ)n = cos nθ + i sin nθ
34. When is De Moivre’s theorem used?
Answer: To find powers and roots of complex numbers.
35. How many nth roots does a complex number have?
Answer: Exactly n distinct roots.
36. How are roots placed in complex plane?
Answer: They are equally spaced on a circle.
37. Is addition of complex numbers commutative?
Answer: Yes.
38. Is multiplication of complex numbers associative?
Answer: Yes.
39. Does zero have a multiplicative inverse?
Answer: No.
40. Why are complex numbers important?
Answer: They help in solving equations which have no real solutions.
41. Give one real-life use of complex numbers.
Answer: Used in electrical engineering and signal processing.
42. Can we compare complex numbers?
Answer: No, complex numbers cannot be compared like real numbers.
