Complex Numbers and Quadratic Equations
CBSE · Class 11 · Mathematics
Quick revision notes for Complex Numbers and Quadratic Equations — CBSE Class 11 Mathematics. Key concepts, formulas, and definitions for last-minute revision.
Key Topics to Revise
Introduction to Complex Numbers
- Complex numbers were introduced to solve equations like x² = -1
- The imaginary unit i is defined as i² = -1
- Every complex number can be written as z = a + bi where a, b are real numbers
Algebra of Complex Numbers
- Addition: (a + bi) + (c + di) = (a + c) + (b + d)i
- Subtraction: (a + bi) - (c + di) = (a - c) + (b - d)i
- Multiplication: (a + bi)(c + di) = (ac - bd) + (ad + bc)i
Powers of i
- i¹ = i, i² = -1, i³ = -i, i⁴ = 1
- The pattern repeats every 4 powers
- For any integer k: i^(4k) = 1, i^(4k+1) = i, i^(4k+2) = -1, i^(4k+3) = -i
Square Roots of Negative Numbers
- √(-a) = i√a for positive real number a
- The principal square root of -1 is i
- √(-a) × √(-b) = -√(ab) when both a and b are positive (different from positive case)
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Sources & Official References
- NCERT Official — ncert.nic.in
- CBSE Academic — cbseacademic.nic.in
- CBSE Official — cbse.gov.in
- National Education Policy 2020 — education.gov.in
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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