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Complex Numbers

Maharashtra Board · Class 11 · Mathematics & Statistics

Quick revision notes for Complex Numbers — Maharashtra Board Class 11 Mathematics & Statistics. Key concepts, formulas, and definitions for last-minute revision.

30 questions20 flashcards5 concepts

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Key Topics to Revise

1

Introduction to Complex Numbers and Imaginary Unit

  • The imaginary unit i is defined as i = √(-1), so i² = -1
  • Powers of i follow a cyclical pattern: i¹ = i, i² = -1, i³ = -i, i⁴ = 1
  • For any positive integer n: i⁴ⁿ = 1, i⁴ⁿ⁺¹ = i, i⁴ⁿ⁺² = -1, i⁴ⁿ⁺³ = -i
2

Operations on Complex Numbers

  • Addition: (a + ib) + (c + id) = (a + c) + i(b + d)
  • Subtraction: (a + ib) - (c + id) = (a - c) + i(b - d)
  • Multiplication: (a + ib)(c + id) = (ac - bd) + i(ad + bc)
3

Square Root of Complex Numbers

  • If √(x + iy) = a + ib, then squaring both sides gives x + iy = (a + ib)²
  • This leads to: x = a² - b² and y = 2ab
  • Solve simultaneously to find a and b
4

Quadratic Equations with Complex Numbers

  • For ax² + bx + c = 0, roots are x = (-b ± √(b² - 4ac))/(2a)
  • If discriminant D = b² - 4ac < 0, roots are complex conjugates
  • Complex roots always occur in conjugate pairs when coefficients are real

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Full Notes

Key Concepts

The imaginary unit i is definedA complex number z =The conjugate of z =AdditionTo find √(x+iy)

Frequently Asked Questions

What are the important topics in Complex Numbers for Maharashtra Board Class 11 Mathematics & Statistics?
Complex Numbers covers several key topics that are frequently asked in Maharashtra Board 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 — Maharashtra Board Class 11 Mathematics & Statistics?
Start by understanding all key concepts. Practise previous year questions from this chapter. Revise formulas and definitions regularly. Use flashcards for quick revision before the exam.

Sources & Official References

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

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All 18 chapters — Maharashtra Board Class 11 Mathematics & Statistics Revision Notes

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