Class 11 Mathematics — Chapter 5: Complex Numbers and Quadratic Equations
66 practice questions · 22 Easy · 22 Medium · 22 Hard
Practise Class 11 Mathematics Chapter 5, "Complex Numbers and Quadratic Equations", with 66 NCERT-aligned multiple-choice questions. The set is split into 22 Easy, 22 Medium and 22 Hard questions, so you can warm up on the fundamentals and then push into the exam-level problems that separate top scorers in CBSE Board exams, JEE Main and JEE Advanced.
"Complex Numbers and Quadratic Equations" is one of the chapters where problem-solving speed, formula recall and step-by-step reasoning really pays off. Each MCQ on this chapter is timed and uses exam-grade marking (+2 correct, −1 wrong, 0 skipped), training the same accuracy-under-pressure that real papers demand. Every question carries a short explanation, so a wrong answer becomes a quick lesson rather than a dead end — the fastest way to close gaps before a test.
Use this chapter as targeted revision: attempt the Easy set first to confirm your basics on Complex Numbers and Quadratic Equations, then move to Medium and Hard to test application and problem-solving. Your accuracy, streaks and XP save automatically, and the chapter feeds into your overall Class 11 Mathematics mastery score. A few sample questions are shown below; sign in free to practise all 66.
Key concepts: Complex Numbers and Quadratic Equations (Class 11 Mathematics)
This chapter introduces complex numbers, their algebra and modulus–argument form, and solves quadratic equations with complex roots.
- Complex number
- A number z = a + ib where i = √(−1); a is the real part, b the imaginary part.
- Algebra & conjugate
- Addition, multiplication and division use i² = −1; the conjugate of a+ib is a−ib.
- Modulus & argument
- |z| = √(a²+b²); the polar form is z = r(cosθ + i sinθ) where θ is the argument.
- Quadratic with complex roots
- When the discriminant b²−4ac < 0, the quadratic has a pair of complex conjugate roots.
- Argand plane
- Complex numbers are represented as points (a, b) on the Argand plane.
Key formulas — Complex Numbers and Quadratic Equations
💡 Exam tips for Complex Numbers and Quadratic Equations
- Rationalise division by multiplying numerator and denominator by the conjugate of the denominator.
- If discriminant < 0, the roots are complex conjugates — write them with i = √(−1).
Sample questions
|3 + 4i| =
√(9 + 16) = 5.
i¹⁰⁰ =
100 = 4·25 ⇒ i¹⁰⁰ = 1.
Conjugate of 2−3i:
Flip the imaginary sign.
Complex Numbers and Quadratic Equations — FAQs
What are the key concepts in Class 11 Mathematics Complex Numbers and Quadratic Equations?+
This chapter introduces complex numbers, their algebra and modulus–argument form, and solves quadratic equations with complex roots. Key ideas include Complex number, Algebra & conjugate, Modulus & argument, Quadratic with complex roots, Argand plane.
What does Class 11 Mathematics Chapter 5 (Complex Numbers and Quadratic Equations) cover on XamBaaz?+
It covers 66 NCERT-aligned MCQs on "Complex Numbers and Quadratic Equations" — 22 Easy, 22 Medium and 22 Hard — each with a timed quiz and an instant explanation, suitable for CBSE Board exams, JEE Main 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 (limited-time launch price), with no per-chapter charges.
How should I revise "Complex Numbers and Quadratic Equations" for the exam?+
Start with the Easy quiz to confirm your fundamentals, then attempt Medium and Hard for application-level practice. Review each explanation, retry the questions you miss, and track your accuracy on this chapter until it is consistently high.
Practise all 66 questions free
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