Question

, show that z1z2z3 are the vertices of an equilateral triangle inscribed in a unit circle. 

Solution

Correct option is

60o

, the origin is the circumcentre of the triangle and circum-radius is 1. Hence by rotating in anti-clockwise direction about O,  

       

  

  

   

   

                     

Squaring and adding,   2 + 2 cos 2B = 1  

    

          

Putting in (i), we get 

            

  

     

  

   

.

SIMILAR QUESTIONS

Q1

Find all the values of the given root:

            

Q2

 are the n, nth roots of unity, 

Q3

If ω is fifth root of unity, then  

     

Q4

, then find the equation whose roots are p and q.

Q5

Find the roots of the equation , whose real part is negative.

Q6

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

  

Q8
Q9

For all complex numbers z1z2 satisfying , the minimum value of 

Q10

The complex numbers z1, z2 and z3 satisfying  are the vertices of a triangle which is