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## Homework Statement

in a given activity: solve for z in C the equation: z^3=1

## Homework Equations

prove that the roots are 1, i, and i^2

## The Attempt at a Solution

using z^3-1=0 <=> Z^3-1^3 == a^3-b^3=(a-b)(a^2+2ab+b^2)

it's clear the solution are 1 and i^2=-1 but i didn't find "i" as a solution by using this method

i need your help please