Complex Numbers - Multiple Choice Questions
| 01 | What is the value of i²? (A) 1 (B) 0 (C) –1 (D) i |
| 02 | If z = 3 + 4i, find the modulus of z. (A) 5i (B) 5 (C) 7 (D) 25 |
| 03 | The conjugate of (2 – 3i) is: (A) 2 + 3i (B) –2 + 3i (C) –2 – 3i (D) 3 – 2i |
| 04 | If z = a + bi, then its conjugate is: (A) –a + bi (B) a – bi (C) –a – bi (D) a + bi |
| 05 | Find the argument (θ) of the complex number 1 + i. (A) 0° (B) 30° (C) 45° (D) 60° |
| 06 | Which of the following is purely imaginary? (A) 2 + 3i (B) 3 – 2i (C) 0 + 5i (D) 5 |
| 07 | What is the real part of (–4 + 3i)? (A) –4 (B) 3 (C) 4 (D) –3 |
| 08 | Multiply (2 + 3i)(1 – 4i). (A) 14 + 5i (B) –14 + 5i (C) 14 – 5i (D) –14 – 5i |
| 09 | Divide (6 + 2i) by (3 – i). (A) 1 + i (B) 2 + 3i (C) 2 + i (D) 3 + 2i |
| 10 | If |z| = 1 and z = a + bi, then: (A) a² + b² = 0 (B) a² + b² = 1 (C) a² + b² = 2 (D) a² – b² = 1 |
| 11 | Find the square of (2 + i). (A) 4 + 4i (B) 3 + 4i (C) 3 + 4i (D) 4 – 3i |
| 12 | If z = 4(cos60° + i sin60°), find the real part. (A) 2 (B) 3 (C) 2 (D) 1 |
| 13 | Which of the following represents a complex number on the imaginary axis? (A) 3 + 0i (B) 0 + 3i (C) 3 + 3i (D) 0 |
| 14 | The polar form of (1 + i) is: (A) √2(cos30° + i sin30°) (B) √2(cos45° + i sin45°) (C) √2(cos60° + i sin60°) (D) √2(cos90° + i sin90°) |
| 15 | The cube roots of unity are: (A) 1, –1, i (B) 1, ω, ω² (C) 1, i, –i (D) 1, –ω, ω² |
| 16 | What is the value of i³? (A) 1 (B) –1 (C) –i (D) i |
| 17 | If z = 5 – 12i, what is |z|? (A) 13i (B) 7 (C) 13 (D) 17 |
| 18 | The complex number 0 + 0i is: (A) Purely real (B) Purely imaginary (C) Both real and imaginary (D) Neither |
| 19 | What is the conjugate of –7i? (A) –7 (B) 7i (C) 7 (D) –7i |
| 20 | If z = 2(cos30° + i sin30°), what is z in rectangular form? (A) 1 + i (B) √3 + i (C) 1 + √3i (D) √3 + √3i |
| 21 | What is the value of i⁴? (A) 1 (B) –1 (C) i (D) –i |
| 22 | If z₁ = 3 + 4i and z₂ = 1 – 2i, what is z₁ + z₂? (A) 4 + 2i (B) 4 + 2i (C) 2 + 6i (D) 4 – 2i |
| 23 | What is the imaginary part of 5 – 3i? (A) 5 (B) –3 (C) 3 (D) –5 |
| 24 | If z = 1 + i, what is z²? (A) 1 + i (B) 2 + 2i (C) 2i (D) 0 |
| 25 | What is the modulus of –3 – 4i? (A) 7 (B) 5 (C) –5 (D) 1 |
| 26 | If z = 2 + 3i, what is z · z̅? (A) 13 (B) 13 (C) 5 (D) –5 |
| 27 | What is the argument of –1? (A) 0° (B) 180° (C) 90° (D) 270° |
| 28 | If z = 4 – 3i, what is 1/z? (A) 4/25 + 3/25i (B) 4/25 – 3/25i (C) 4/25 + 3/25i (D) 4/7 – 3/7i |
| 29 | What is the value of i¹⁰? (A) i (B) –i (C) 1 (D) –1 |
| 30 | If z = 1 + √3i, what is |z|? (A) 1 (B) 2 (C) 2 (D) 4 |
| 31 | What is the polar form of –i? (A) cos0° + i sin0° (B) cos90° + i sin90° (C) cos270° + i sin270° (D) cos180° + i sin180° |
| 32 | If ω is a cube root of unity, what is 1 + ω + ω²? (A) 1 (B) ω (C) 0 (D) –1 |
| 33 | What is the conjugate of 5? (A) 5 (B) –5 (C) 5i (D) –5i |
| 34 | If z = 3 + 4i, what is the argument of z? (A) 30° (B) 45° (C) 53.13° (D) 60° |
| 35 | What is the product of (2 + i) and (2 – i)? (A) 3 (B) 4 (C) 5 (D) 4 + 4i |
| 36 | If z = x + iy, what is z + z̅? (A) 2iy (B) 2x (C) 2xi (D) x² + y² |
| 37 | What is the value of i⁷? (A) 1 (B) –1 (C) –i (D) i |
| 38 | If z = 1 – i, what is z³? (A) 1 – i (B) –2 – 2i (C) –2 – 2i (D) 2 + 2i |
| 39 | What is the modulus of 1/(1 + i)? (A) 1 (B) 1/√2 (C) √2 (D) 2 |
| 40 | If z₁ = 2 + 3i and z₂ = 4 – i, what is z₁/z₂? (A) 5/17 + 14/17i (B) 5/17 + 14/17i (C) 14/17 + 5/17i (D) 5/17 – 14/17i |
| 41 | What is the argument of i? (A) 0° (B) 90° (C) 180° (D) 270° |
| 42 | If z = 2(cos45° + i sin45°), what is z²? (A) 2(cos90° + i sin90°) (B) 4(cos90° + i sin90°) (C) 2(cos45° + i sin45°) (D) 4(cos45° + i sin45°) |
| 43 | What is the value of (1 + i)⁴? (A) 4 (B) –4 (C) –4 (D) 4i |
| 44 | If z = 3 – 4i, what is the real part of 1/z? (A) 3/25 (B) 3/25 (C) 4/25 (D) –4/25 |
| 45 | What is the polar form of –1 – i? (A) √2(cos135° + i sin135°) (B) √2(cos225° + i sin225°) (C) √2(cos315° + i sin315°) (D) 2(cos225° + i sin225°) |
| 46 | If ω is a cube root of unity, what is ω³? (A) 1 (B) ω (C) ω² (D) 0 |
| 47 | What is the conjugate of –2 + 5i? (A) 2 – 5i (B) –2 – 5i (C) 2 + 5i (D) –2 + 5i |
| 48 | If z = 4 + 3i, what is |z|²? (A) 7 (B) 5 (C) 25 (D) 16 |
| 49 | What is the value of i²⁰? (A) 1 (B) –1 (C) i (D) –i |
| 50 | If z = 1 + i, what is the argument of z²? (A) 45° (B) 90° (C) 135° (D) 180° |
