Math Problem Statement

Find the value of (-1 + i√3)^10 using De Moivre's theorem.

Solution

To solve the expression (−1+i3)10(-1 + i\sqrt{3})^{10} using De Moivre's Theorem, we first need to convert the complex number to polar form. Let's break down the steps:

Step 1: Convert to polar form

A complex number z=x+iyz = x + iy can be written in polar form

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Math Problem Analysis

Mathematical Concepts

Complex Numbers
Polar Coordinates
Exponents

Formulas

z = r(cosθ + isinθ)
(r * e^(iθ))^n = r^n * e^(i * n * θ)

Theorems

De Moivre's Theorem

Suitable Grade Level

Grades 11-12

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