Chapter Exam

Chapter-4 Complex Numbers and Quadratic Equations — Online MCQ Test

Q: What is the value of i²?

Answer: A. -1 — By definition, the imaginary unit i is defined such that i² = -1.

Q: If z = 3 + 4i, what is the real part of z?

Answer: B. 3 — In the complex number z = a + bi, a is the real part and b is the imaginary coefficient; here a = 3.

Q: If z₁ = 2 + 3i and z₂ = 1 - i, find z₁ + z₂.

Answer: A. 3 + 2i — z₁ + z₂ = (2 + 3i) + (1 - i) = (2+1) + (3-1)i = 3 + 2i.

Q: If z = (1 + 2i)/(1 - i), find z in the form a + bi.

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.

Q: For what value of k does x² - 2x + k = 0 have one real and one imaginary root?

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.

MATHS · Grade 11 · CBSE(NCERT)

Practice Chapter-4 Complex Numbers and Quadratic Equations with a free chapter-wise online MCQ test for CBSE(NCERT) Grade 11 MATHS. 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.

Questions

20m

Time Limit

Attempts Left

10 random questions from this chapter (mixed difficulty)
Questions you've seen before won't repeat until the pool resets
You have 20 minutes — exam auto-submits when time is up
Maximum 3 attempts per chapter
Results and explanations shown immediately after submission

New here? Register free — includes 3 free chapter exams.

Chapter-4 Complex Numbers and Quadratic Equations — Important Questions & Answers (FAQ)

Frequently asked questions from CBSE(NCERT) Grade 11 MATHS — Chapter-4 Complex Numbers and Quadratic Equations, with answers and explanations. These are sample questions; the exam has its own separate question set.

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.

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.

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.

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.

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.