Math Problem Statement
let z=1/3 + ((square root of 3) /2)i. solve for (z̄)^4. Note z̄ is the conjugate of z
Solution
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Math Problem Analysis
Mathematical Concepts
Complex Numbers
Conjugates
Polar Form
Powers of Complex Numbers
Formulas
Complex Conjugate: z̄ = a - bi
Modulus: |z| = sqrt(a^2 + b^2)
Argument: θ = tan^(-1)(b/a)
De Moivre's Theorem: (r(cosθ + isinθ))^n = r^n(cos(nθ) + isin(nθ))
Theorems
De Moivre's Theorem
Polar Form of Complex Numbers
Suitable Grade Level
College level (or advanced high school students)