Math Problem Statement

Solution

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Math Problem Analysis

Mathematical Concepts

Complex Numbers
De Moivre's Theorem
Polar Form of Complex Numbers

Formulas

(1 + i)^4 = (√2)^4 * cis(π) = 4 * (-1) = -4
1 + i√3 in polar form
De Moivre's Theorem: (r cis θ)^n = r^n * cis(nθ)
Euler's Formula: e^(iθ) = cos θ + i sin θ

Theorems

De Moivre's Theorem
Euler's Formula

Suitable Grade Level

Undergraduate (Complex Numbers & Advanced Algebra)

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