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Given the complex numbers a and b such that |a|=|b|=|a-b|=1. The numbers a and b verifiy the equaliy: a) a^2+b^2=ab b)a^2+b^2=3ab c)a^2+ab+b^2=0 d)a^2+ab+b^2=1 I mention that there may be several correct options so all 4 conditions must be checked if they are true or not, I also need a complete solution

Given the complex numbers a and b such that |a|=|b|=|a-b|=1. The numbers a and b verifiy the equaliy: a) a^2+b^2=ab b)a^2+b^2=3ab c)a^2+ab+b^2=0 d)a^2+ab+b^2=1 I mention that there may be several correct options so all 4 conditions must be checked if they are true or not, I also need a complete solution

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 35E
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Given the complex numbers a and b such that |a|=|b|=|a-b|=1.

The numbers a and b verifiy the equaliy:

a) a^2+b^2=ab

b)a^2+b^2=3ab

c)a^2+ab+b^2=0

d)a^2+ab+b^2=1

I mention that there may be several correct options so all 4 conditions must be checked if they are true or not, I also need a complete solution and not just to check the correct option.

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