Skip to main content
Super TutorResources
Chapter 4 of 14
QuestionsNotesFlashcardsSummaryFormulasQuizConceptsSyllabusPlan
Syllabus

Complex Numbers and Quadratic Equations

CBSE · Class 11 · Mathematics

Complete topic list for Complex Numbers and Quadratic Equations in CBSE Class 11 Mathematics. Key concepts, sub-topics, and what to focus on for board exams.

168 questions54 flashcards5 concepts

Interactive on Super Tutor

Studying Complex Numbers and Quadratic Equations? Get the full interactive chapter.

Quizzes, flashcards, AI doubt-solver and a step-by-step study plan — built for syllabus and more.

Try Super Tutor — Free

1,000+ Class 11 students started this chapter today

4 Topics · CBSE Class 11 Mathematics

Topics in Complex Numbers and Quadratic Equations

1

1. Need for Complex Numbers

  • The equation x^2 + 1 = 0 has no real solution because the square of every real number is non-negative.
  • The main objective is to solve ax^2 + bx + c = 0 where D = b^2 - 4ac < 0, which is not possible in real numbers.
  • To handle such equations, the number system is extended by introducing i, where i^2 = -1.
2

2. Complex Numbers and Their Parts

  • A complex number has the form z = a + ib, where a and b are real numbers.
  • For z = a + ib, a is the real part and b is the imaginary part.
  • Two complex numbers z1 = a + ib and z2 = c + id are equal if a = c and b = d.
3

3. Algebra of Complex Numbers

  • The sum of two complex numbers is again a complex number.
  • Addition of complex numbers is commutative and associative.
  • There is an additive identity 0 + i0, written as 0.
4

4. Powers of i and Square Roots of Negative Numbers

  • i^3 = -i and i^4 = 1.
  • i^5 = i and i^6 = -1.
  • For negative powers, i^-1 = -i, i^-2 = -1, i^-3 = i, and i^-4 = 1.

Key Concepts

Central concept: Complex Numbers and Quadratic Equations

Need for complex numbersImaginary unit iComplex number formEquality of complex numbersAlgebra of complex numbersProperties of operationsAdditive identity and inverseMultiplicative identity and inverse

Frequently Asked Questions

What are the important topics in Complex Numbers and Quadratic Equations for CBSE Class 11 Mathematics?
Complex Numbers and Quadratic Equations covers several key topics that are frequently asked in CBSE Class 11 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Complex Numbers and Quadratic Equations — CBSE Class 11 Mathematics?
Understand the core concepts first, then work through the 168 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

More resources for Complex Numbers and Quadratic Equations

All 14 chapters — CBSE Class 11 Mathematics Syllabus

For serious students

Get the full Complex Numbers and Quadratic Equations chapter — for free.

Quizzes, flashcards, AI doubt-solver and a step-by-step study plan for CBSE Class 11 Mathematics.

Try Super Tutor Free
Try the full chapter — Free