Unit 3 • Class 12Mathematics (Mat.402)
Complex Numbers & De Moivre's Theorem
मिश्र संख्या तथा डि मोइभरको प्रमेय
Polar and exponential forms, De Moivre theorem for rational exponents, roots of complex numbers, cube roots of unity (1, ω, ω²) and their algebraic properties.
Lesson Summary & Key Concepts
Polar representation of complex numbers, proof and application of De Moivre's Theorem for integral and rational indices, extraction of roots, and properties of cube roots of unity (1, ω, ω²).
Textbook Exercises & Solutions
Showing 1 of 1 Solved QuestionsQuestion 1• 4 Marks
Quick Revision Takeaways
Common Exam Pitfalls to Avoid
⚠️ Common Error: Forgetting that (cos θ - i sin θ)ⁿ = cos(nθ) - i sin(nθ).
✓ Correct Approach: Write cos θ - i sin θ as cos(-θ) + i sin(-θ) before applying De Moivre.
Why: Standard De Moivre requires a plus sign between real and imaginary parts.
Previous LessonBinomial Theorem & Exponential/Logarithmic Series
Next LessonSequence and Series & Mathematical Induction
Content Provenance & Verification
Editorial Verified & Published
Original Author / ContributorNEB Notes Nepal Academic Team
Verified BySenior Subject Specialist (TU / NEB Panel)
Curriculum Versionv1.0 (CDC 2078/2080 Grid)
Last Verified Date2026-10-23
Legitimate Official Curriculum References
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