Q. Let `z_1` and `z_2` be nth roots of unity which subtend a right angle at the origin, then n must be the form `4k`.

Q. Let z_1 and z_2 be nth roots of unity which subtend a right angle at the origin, then n must be the form of .

Let z_1 and z_2 be theroots of the equation z^2+az+b=0 z being compex. Further, assume that the origin z_1 and z_2 form an equilatrasl triangle then

If z_(1),z_(2),z_(3) are the vertices of an isoscles triangle right angled at z_(2) , then

If z_(1) and z_(2) are two n^(th) roots of unity, then arg (z_(1)/z_(2)) is a multiple of

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

If z_(0),z_(1) represent points P and Q on the circle |z-1|=1 taken in anticlockwise sense such that the line segment PQ subtends a right angle at the center of the circle, then z_(1)=

If z_0,z_1 represent points P ,Q on the locus |z-1|=1 and the line segment P Q subtends an angle pi/2 at the point z=1 then z_1 is equal to (a) 1+i(z_0-1) (b) i/(z_0-1) (c) 1-i(z_0-1) (d) i(z_0-1)

z_1, z_2 and z_3 are the vertices of an isosceles triangle in anticlockwise direction with origin as in center , then prove that z_2, z_1 and kz_3 are in G.P. where k in R^+dot

Let z_(1) and z_(2) be the roots of the equation z^(2)+pz+q=0 . Suppose z_(1) and z_(2) are represented by points A and B in the Argand plane such that angleAOB=alpha , where O is the origin. Statement-1: If OA=OB, then p^(2)=4q cos^(2)alpha/2 Statement-2: If affix of a point P in the Argand plane is z, then ze^(ia) is represented by a point Q such that anglePOQ =alpha and OP=OQ .

Let z_1 and z_2 be two non - zero complex numbers such that z_1/z_2+z_2/z_1=1 then the origin and points represented by z_1 and z_2