Quiz for Complex Numbers

Q1: What is the modulus of the complex number z = 3 + 4i?

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

Q2: What is the conjugate of z = 2 - 5i?

A. 2 + 5i B. -2 + 5i C. 2 - 5i D. -2 - 5i

Q3: If z = a + ib, then Re(z) = ?

A. a B. b C. -a D. -b

Q4: What is the value of i^4?

A. i B. -1 C. 1 D. -i

Q5: Which of the following is equal to (1 + i)^2?

A. 2i B. 1 + 2i C. 2 D. 2i + 1

Q6: Which point represents z = -1 + i on the Argand plane?

A. Second quadrant B. First quadrant C. Third quadrant D. Fourth quadrant

Q7: If z1 = 2 + 3i and z2 = 1 - 2i, what is z1 + z2?

A. 3 + i B. 1 + 5i C. 3 - i D. 2 + i

Q8: The principal argument of -1 + √3i is?

A. π/3 B. 2π/3 C. 4π/3 D. 5π/3

Q9: What is the square of i?

A. -1 B. i C. 1 D. -i

Q10: If z = cosθ + i sinθ, what is |z|?

A. cosθ B. sinθ C. 1 D. 0

Q11: The polar form of z = 1 + i is?

A. √2 (cos π/4 + i sin π/4) B. 1 + i C. 2 (cos π/2 + i sin π/2) D. √2 (cos π/2 + i sin π/4)

Q12: If z = x + iy lies on the imaginary axis, then x = ?

A. 0 B. 1 C. y D. -y

Q13: What is the product of z and its conjugate if z = 3 + 4i?

A. 25 B. 7 C. 0 D. 5

Q14: If z = r(cosθ + i sinθ), then z^n = ?

A. r^n (cos nθ + i sin nθ) B. r^n (cos θ + i sin θ) C. r (cos nθ + i sin nθ) D. r^n (cosθ + i sinθ)^n

Q15: Let z = -√3 + i. Then the argument of z is?

A. 5π/6 B. 2π/3 C. π/3 D. π/6

Q16: Which of the following is purely imaginary?

A. 0 + 2i B. 2 + 0i C. -1 + i D. 1 - 1

Q17: What is the real part of (1 + i)^4?

A. 0 B. 4 C. 8 D. 2

Q18: If z = a + ib and |z| = 0, then?

A. a = b = 0 B. a = b C. a ≠ 0 D. b = 1

Q19: i^20 is equal to?

A. 1 B. -1 C. i D. -i

Q20: What is the multiplicative inverse of 1 + i?

A. (1 - i)/2 B. 1 + i C. 2 + 2i D. 1 - i