Home
Class 11
MATHS
Let z(1) and z(2) be n^(th ) roots of un...

Let `z_(1)` and `z_(2)` be `n^(th )` roots of unity which subtend a right angle at the origin. Then n must be of the form.

A

4k+2

B

4k+1

C

4k

D

4k+3

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Similar Questions

Explore conceptually related problems

The locus of the mid-points of chords of the circle x^2+y^2 =4 , which subtend a right angle at the origin, is:

Let AB be a chord of the circle x^2+y^2=a^2 subtending a right angle at the centre. Then the locus of the centroid of triangle PAB as P moves on the circle is:

Let z_(1) and z_(2) be two roots of the equation z^(2)+az+b=0 , z being complex number, assume that the origin z_(1) and z_(2) form an equilateral triangle , then

The locus of the midpoint of a chord of the circle x^(2)+y^(2) = 4 which subtends a right angle at the origin is

If z_(1),z_(2)andz_(3) are the affixes of the vertices of a triangle having its circumcentre at the origin. If zis the affix of its orthocentre, prove that Z_(1)+Z_(2)+Z_(3)-Z=0.

Let z_1 \and\ z_2 be the roots of the equation z^2+p z+q=0, where the coefficients p \and \q may be complex numbers. Let A \and\ B represent z_1 \and\ z_2 in the complex plane, respectively. If /_A O B=theta!=0 \and \O A=O B ,\where\ O is the origin, prove that p^2=4q"cos"^2(theta//2)dot

Complex numbers z_(1),z_(2)andz_(3) are the vertices A,B,C respectivelt of an isosceles right angled triangle with right angle at C. show that (z_(1)-z_(2))^(2)=2(z_1-z_(3))(z_(3)-z_(2)).

If P_x,P_y and P_z are the magnitudes of forces on a body actin mutually at right angles to each other, then represent the resultant force on the body in (1) a scaler and (2) vector form.

If z_(1),z_(2)and z_(3) are the vertices of an equilateral triangle with z_0 as its circumcentre , then changing origin to z_0 ,show that z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=0, where z_(1),z_(2),z_(3), are new complex numbers of the vertices.

Let z_(1) and z_(2) be two distinct complex numbers and let z=(1-t)z_(1)+tz_(2) for some real number t with 0 lt t lt 1 . If Arg (w) denotes the principal argument of a non zero complex number w , then