Chapter-4 Complex Numbers and Quadratic Equations — Online MCQ Test
MATHS · Grade 11 · CBSE(NCERT)
Practice Chapter-4 Complex Numbers and Quadratic Equations with a free chapter-wise online MCQ test.
This chapter covers: Imaginary unit (i) - Real and imaginary parts - Conjugate - Modulus - Argand plane - Polar representation - Square root of negative numbers - Quadratic formula.
AI-generated questions from basic to board-exam level, with instant results and explanations.
Chapter-4 Complex Numbers and Quadratic Equations — Important Questions & Answers
What is the value of i²?
- A. -1
- B. 1
- C. i
- D. -i
Answer: A. -1
By definition, the imaginary unit i is defined such that i² = -1.
By definition, the imaginary unit i is defined such that i² = -1.
If z = 3 + 4i, what is the real part of z?
- A. 4
- B. 3
- C. 7
- D. 12
Answer: B. 3
In the complex number z = a + bi, a is the real part and b is the imaginary coefficient; here a = 3.
In the complex number z = a + bi, a is the real part and b is the imaginary coefficient; here a = 3.
If z₁ = 2 + 3i and z₂ = 1 - i, find z₁ + z₂.
- A. 3 + 2i
- B. 1 + 4i
- C. 3 - 2i
- D. 2 + 3i
Answer: A. 3 + 2i
z₁ + z₂ = (2 + 3i) + (1 - i) = (2+1) + (3-1)i = 3 + 2i.
z₁ + z₂ = (2 + 3i) + (1 - i) = (2+1) + (3-1)i = 3 + 2i.
If z = (1 + 2i)/(1 - i), find z in the form a + bi.
- A. -1/2 + 3i/2
- B. 1/2 - 3i/2
- C. -1 + 3i
- D. 1 + 3i
Answer: A. -1/2 + 3i/2
Multiply by conjugate: [(1+2i)(1+i)]/[(1-i)(1+i)] = [1+i+2i-2]/2 = [-1+3i]/2 = -1/2 + 3i/2.
Multiply by conjugate: [(1+2i)(1+i)]/[(1-i)(1+i)] = [1+i+2i-2]/2 = [-1+3i]/2 = -1/2 + 3i/2.
For what value of k does x² - 2x + k = 0 have one real and one imaginary root?
- A. k = 1
- B. k > 1
- C. k = 0
- D. No such k exists
Answer: D. No such k exists
For a quadratic with real coefficients, roots are either both real or both complex conjugates; mixed real and non-real imaginary roots are impossible.
For a quadratic with real coefficients, roots are either both real or both complex conjugates; mixed real and non-real imaginary roots are impossible.