Complex Numbers and Quadratic Equations — Class 11 MCQs with Answers
Class 11 CBSE Mathematics · Chapter 5
90 practice questions · 30 Easy · 30 Medium · 30 Hard · Updated
Practise the most important Class 11 CBSE Mathematics questions from Chapter 5, "Complex Numbers and Quadratic Equations". You get 9 timed quizzes made from 90 NCERT-based MCQs, with answers and explanations. The questions are split into 30 Easy, 30 Medium and 30 Hard. Warm up on the basics, then move on to the exam-level questions that set top scorers in CBSE & Maharashtra HSC Board exams, JEE Main, MHT-CET and JEE Advanced apart.
To score well in "Complex Numbers and Quadratic Equations", focus on fast problem-solving, formula recall and step-by-step working. Each MCQ here is timed and uses exam-style marking (+4 correct, −1 wrong, 0 skipped). This trains you to stay accurate under time pressure, as real papers need. Every question has a short explanation, so a wrong answer becomes a quick lesson. It is the fastest way to fix gaps before a test.
Use this chapter for focused revision. Start with the Easy set to check your basics on Complex Numbers and Quadratic Equations, then move to Medium and Hard to practise applying them. Your accuracy, streaks and XP save automatically. This chapter also adds to your overall Class 11 Mathematics mastery score. 14 sample questions are solved in full below, with the answer and a worked explanation. Sign in free to start practising.
Key concepts: Complex Numbers and Quadratic Equations (Class 11 Mathematics)
When x²+1=0 has no real root, the imaginary unit i=√(−1) extends the reals to the complex numbers z=a+ib. This chapter develops their algebra and conjugates, the modulus–argument (polar) form on the Argand plane, and returns to quadratics, showing that a negative discriminant delivers a pair of complex-conjugate roots.
- Imaginary unit
- i=√(−1) with i²=−1. Its powers cycle with period four — i, −1, −i, 1 — so iⁿ depends only on n taken modulo 4.
- Complex number
- z=a+ib with a,b real; a=Re(z) is the real part and b=Im(z) the imaginary part. z is purely imaginary when a=0.
- Algebra of complex numbers
- Add and subtract componentwise; multiply using i²=−1. Complex numbers form a field, obeying the usual commutative and distributive laws.
- Conjugate
- The conjugate of z=a+ib is z̄=a−ib. Then z·z̄ = a²+b² = |z|² is real, which is the key to dividing complex numbers.
Complex Numbers and Quadratic Equations — important questions & MCQs with answers (Class 11 Mathematics)
14 solved questions from this chapter's difficulty levels, each with its answer and explanation. The other 76 are timed and scored when you sign in.
- Q1Easy
Value of i² is:
A.iB.1C.0D.−1✓ CorrectAnswer: D. −1
Explanation: i is defined so that i² = −1 — the whole point of introducing imaginary numbers. Mixing it up with i⁴ = 1 (two squarings later) is the common slip.
- Q2Easy
Roots of x²−5x+6=0:
A.1, 6B.−2, −3C.2 and 3✓ CorrectD.5, 1Answer: C. 2 and 3
Explanation: Factor x²−5x+6 as (x−2)(x−3), so the roots are 2 and 3 — check: sum 5 matches −(−5)/1 and product 6 matches 6/1. Picking the sign-flipped pair, −2 and −3, is the usual mix-up.
- Q3Easy
A complex number is of the form:
A.a + b onlyB.a + ib where a, b ∈ R and i² = −1✓ CorrectC.abD.Always imaginaryAnswer: B. a + ib where a, b ∈ R and i² = −1
Explanation: A complex number is written a + ib with a, b real and i defined by i² = −1 — a is the real part, b the imaginary part. Writing it as just a+b drops the i and loses the imaginary part entirely.
- Q4Easy
Conjugate of z = a + ib is:
A.a − ib✓ CorrectB.−a + ibC.−a − ibD.b + iaAnswer: A. a − ib
Explanation: The conjugate z̄ of z = a + ib flips only the imaginary part's sign: z̄ = a − ib, with the real part unchanged. Flipping the real part too, giving −a+ib, is the trap.
- Q5Easy
|z| where z = a + ib:
A.a − bB.a + bC.√(a² + b²)✓ CorrectD.abAnswer: C. √(a² + b²)
Explanation: The modulus of z = a+ib is √(a²+b²) — always real and non-negative, since it's a distance from the origin. Forgetting the square root and writing a²+b² is the common mistake.
- Q6Easy
Argand plane represents complex numbers as points with:
A.Polar onlyB.Real on y-axisC.Both on same axisD.Real part on x-axis, imaginary part on y-axis✓ CorrectAnswer: D. Real part on x-axis, imaginary part on y-axis
Explanation: On the Argand plane, the real part of z is plotted on the x-axis and the imaginary part on the y-axis — the same layout as ordinary Cartesian coordinates. Swapping the two axes is the usual confusion.
- Q7Medium
|3+4i| =
A.5✓ CorrectB.7C.25D.4Answer: A. 5
Explanation: Modulus of a+bi is √(a²+b²), always real and non-negative: √(3²+4²) = √25 = 5. Forgetting the square root and stopping at 25 is the common trap.
- Q8Medium
Discriminant of ax²+bx+c=0:
A.−b/2aB.4ac−b²C.b²−4ac✓ CorrectD.b/aAnswer: C. b²−4ac
Explanation: The discriminant of ax²+bx+c is b²−4ac; its sign tells you whether the roots are real or complex. Writing it as 4ac−b² flips the sign and gives the wrong nature of roots.
- Q9Medium
Conjugate of (z₁ + z₂) equals:
A.z̄₁ · z̄₂B.z̄₁ − z̄₂C.z̄₁ + z̄₂✓ CorrectD.z₁ + z₂Answer: C. z̄₁ + z̄₂
Explanation: Conjugation distributes over addition: the conjugate of z₁+z₂ is z̄₁+z̄₂ — flip each imaginary part separately. Leaving the sum un-conjugated, as plain z₁+z₂, misses that both parts flip.
- Q10Medium
|z₁ · z₂| equals:
A.|z₁| / |z₂|B.|z₁| + |z₂|C.|z₁| · |z₂|✓ CorrectD.|z₁ − z₂|Answer: C. |z₁| · |z₂|
Explanation: Modulus is multiplicative: |z₁·z₂| = |z₁|·|z₂|. Adding the moduli instead of multiplying them is the common trap.
- Q11Medium
Distance from origin to point representing z is:
A.Im(z)B.Re(z)C.|z|✓ CorrectD.arg(z)Answer: C. |z|
Explanation: The modulus |z| is the distance from the origin to the point representing z in the Argand plane. Confusing it with the argument, which measures angle not distance, is the trap.
- Q12Hard
Conjugate of 2−3i:
A.3−2iB.−2+3iC.−2−3iD.2+3i✓ CorrectAnswer: D. 2+3i
Explanation: The conjugate of a+bi flips only the sign of the imaginary part: 2−3i becomes 2+3i. Swapping the real and imaginary parts instead, landing on 3−2i, is the trap distractor.
- Q13Hard
For ax²+bx+c=0, sum of roots =
A.c/aB.−b/a✓ CorrectC.b/aD.−c/aAnswer: B. −b/a
Explanation: For ax²+bx+c=0, the sum of roots is −b/a and the product is c/a — dropping that leading minus sign, giving b/a instead, is the usual error.
- Q14Hard
For complex z₁, z₂: |z₁ + z₂| ≤ ?
A.|z₁| − |z₂|B.|z₁| + |z₂|✓ CorrectC.|z₁| · |z₂|D.|z₁|Answer: B. |z₁| + |z₂|
Explanation: The triangle inequality for complex numbers states |z₁+z₂| ≤ |z₁|+|z₂| — the direct path is never longer than the sum of two legs. Reversing it into a lower bound like |z₁|−|z₂| gets the direction wrong.
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Start this chapter free →Complex Numbers and Quadratic Equations — FAQs
What are the key concepts in Class 11 Mathematics Complex Numbers and Quadratic Equations?+
When x²+1=0 has no real root, the imaginary unit i=√(−1) extends the reals to the complex numbers z=a+ib. This chapter develops their algebra and conjugates, the modulus–argument (polar) form on the Argand plane, and returns to quadratics, showing that a negative discriminant delivers a pair of complex-conjugate roots. Key ideas include Imaginary unit, Complex number, Algebra of complex numbers, Conjugate.
What does Class 11 Mathematics Chapter 5 (Complex Numbers and Quadratic Equations) cover on XamBaaz?+
It has 90 NCERT-based MCQs on "Complex Numbers and Quadratic Equations": 30 Easy, 30 Medium and 30 Hard. Together they make 9 timed quizzes, and you never get the same set twice. Every question has an instant explanation. They help you prepare for CBSE & Maharashtra HSC Board exams, JEE Main, MHT-CET and JEE Advanced.
Are these "Complex Numbers and Quadratic Equations" questions free to practise?+
Yes. Sign in with Google to practise "Complex Numbers and Quadratic Equations" free. Full unlimited access is ₹999/year on a launch offer until 1 December 2026. No chapter is charged separately.
How should I revise "Complex Numbers and Quadratic Equations" for the exam?+
Start with the Easy quiz to check your basics, then try Medium and Hard to practise applying them. There are 9 timed quizzes on this chapter, so you can come back for a fresh set instead of one you have seen. Read each explanation, retry the questions you miss, and track your accuracy until it stays high.
Are these "Complex Numbers and Quadratic Equations" MCQs available with answers?+
Yes. 14 sample questions are shown here in full, each with the correct option and a step-by-step "Why" explanation. Sign in free with Google to start practising, with instant scoring.
Is there negative marking in the "Complex Numbers and Quadratic Equations" quizzes?+
Yes. The timed quizzes use exam-style marking: +4 for a right answer, −1 for a wrong one and 0 for a skip, the same negative marking as JEE Main and JEE Advanced. MHT-CET and CBSE board papers have no negative marking. Our mocks for those are scored their way.
What are the important questions from Complex Numbers and Quadratic Equations (Class 11 Mathematics)?+
The questions that matter most test Imaginary unit, Complex number, Algebra of complex numbers, Conjugate. This page shows 14 solved important MCQs with answers and explanations; all 90 questions on the chapter are available as timed quizzes once you sign in.
Is there an online quiz for Complex Numbers and Quadratic Equations?+
Yes — Class 11 Mathematics Complex Numbers and Quadratic Equations has timed online quizzes at Easy, Medium and Hard levels, with instant scoring and a worked explanation on every question. The first quiz on the chapter is free.