Math Problem Statement

Hitung bentuk pangkat dan akar pangkat dari bilangan kompleks berikut

Solution

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Math Problem Analysis

Mathematical Concepts

Complex Numbers
Polar Form
Exponents
Roots

Formulas

Polar form: z = r(cos θ + i sin θ)
Modulus: r = |z| = √(a^2 + b^2)
Argument: θ = arg(z)
Exponentiation: z^n = r^n (cos(nθ) + i sin(nθ))
Nth Root: z_k^(1/n) = r^(1/n) (cos((θ + 2kπ)/n) + i sin((θ + 2kπ)/n))

Theorems

De Moivre's Theorem

Suitable Grade Level

Grades 11-12 and undergraduate math courses