a problem on complex numbers
  
 
     
     
             
                 
 
 
         
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 Let $wneq 1$  and $w^{13} = 1$ .    If $a = w+ w^3 + w^4 + w^{-4} + w^{-3} + w^{-1}$  and $b = w^2+ w^5 + w^6 + w^{-6} + w^{-5} + w^{-2}$ , then the quadratic equation whose roots are $a$  and $b$  is ... ?   I got $w=cos(frac{2pi}{13})+isin(frac{2pi}{13})$  And then I found $a$  and $b$  in trigonometric form. But when I multiplied them to get the product of roots it gets very difficult. How to solve it?      
 
         
             
                 complex-numbers 
             
         
 
     
         
             
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         edited 2 days ago 
     
     
         
     
     
         Andrei 
         
             11.3k 2 10 26 
         
     
                 
             
 
     
         asked 2 days ago 
     
     
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