Question

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

Solution

Correct option is

Obtuse-angled isosceles

Taking mode of both sides of given relation,

             

Hence ∆ is isosceles.  

       

  Anticlocklwise rotation implies that ∠ABC = 60o

Hence isosceles ∆

SIMILAR QUESTIONS

Q1

 are the n, nth roots of unity, 

Q2

If ω is fifth root of unity, then  

     

Q3

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

Q4

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

Q5

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

  

Q7
Q8

For all complex numbers z1z2 satisfying , the minimum value of 

Q9

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

Q10

 

Find the complex numbers z which simultaneously satisfy the equation  

                     .