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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. I have no other additional informations for that problem this is everything i have. Thanks i advance

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. I have no other additional informations for that problem this is everything i have. Thanks i advance

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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.

I have no other additional informations for that problem this is everything i have.

Thanks i advance.

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