Let z1 and z2 be nth Roots Of Unity Which Subtend A Right Angle At The Origin. Then n must Be Of The Form   

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Question

Let z1 and z2 be nth roots of unity which subtend a right angle at the origin. Then n must be of the form

  

Solution

Correct option is

4k

  

                  

 where r varies from 0 to n – 1 and each root is unimodular as   

,   

.  

    

.

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