Complex Numbers and De Moivre’s Theorem
Kerala Board · Class 12 · Mathematics
Quick revision notes for Complex Numbers and De Moivre’s Theorem — Kerala Board Class 12 Mathematics. Key concepts, formulas, and definitions for last-minute revision.
Key Topics to Revise
Introduction to Complex Numbers and Powers of i
- Complex number z = a + bi where a, b ∈ R and i = √(-1)
- Real part: Re(z) = a, Imaginary part: Im(z) = b
- If a = 0 and b ≠ 0: purely imaginary number
Complex Conjugate and Equality
- Conjugate of z = a + bi is z̄ = a - bi
- Two complex numbers are equal iff their real and imaginary parts are equal
- Properties: z̄̄ = z, if z is real then z̄ = z, if z is purely imaginary then z̄ = -z
Modulus of Complex Numbers
- Modulus |z| = √(a² + b²) for z = a + bi
- Geometric interpretation: distance from origin to point (a,b)
- Properties: |z| = 0 ⟺ z = 0, |z| = |z̄| = |-z|, |z₁z₂| = |z₁||z₂|
Argand Plane Representation
- Complex number z = a + bi represented as point (a,b) in coordinate plane
- x-axis: real axis, y-axis: imaginary axis
- Addition represented by parallelogram law
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Sources & Official References
- Kerala Board of Public Examinations — keralapareekshabhavan.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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