Math Problem Statement
(√3-2)^n=2^n(cos(nπ/6)-i*sin(nπ/6))Prove
Solution
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Math Problem Analysis
Mathematical Concepts
Complex Numbers
Polar Form
Trigonometry
Exponential Functions
Formulas
Euler's formula: e^{iθ} = cos(θ) + i*sin(θ)
De Moivre's Theorem: (r(cos θ + i*sin θ))^n = r^n(cos(nθ) + i*sin(nθ))
Modulus of a complex number: |z| = √(a^2 + b^2)
Theorems
De Moivre's Theorem
Euler's Formula
Suitable Grade Level
Undergraduate or advanced high school (Grades 11-12)
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