Question

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

Solution

Correct option is

4k

The n, nth roots of unity are given by

where k1 and k2 are distinct integers from the set {0, 1, 2, 3, …n – 1}.

As z1 and z2 subtend a right angled at the origin, therefore,

So, n = 4 (a positive integer).

SIMILAR QUESTIONS

Q1

The sum of the series

 

Q2
Q4
Q5

The point represented by the complex number 2 – I is rotated about origin through an angle in the clockwise direction. The complex number corresponding to new position of the point is

Q6

                                    

Q7

For all complex number z1, z2 satisfying |z1| = 12 and |z2 – 3 – 4i| = 5, the minimum value of |z1 – z2| is

Q8
Q10

The locus of the centre of a circle which touches the circles |z – z1=a and |z – z2| = b externally (z, z1 and z2 are complex numbers) will be