The points `A_1 (z_1), A_2,(z_2), ..., A_(3n)(z_(3n))` forma regular polygon. `P(z_0)` is the centre of thepolygon. Prove that `z_1^2+z_2^2+.......+z_(3n)^2=3nz_0^2`

If z_(1) , z_(2) , z_(3) are the vertices of an equilateral triangle with centroid at z_0 show that z_(1)^(2) + z_(2)^(2) + z_(3)^(2) = 3 z_(0)^(2)

Given z_(1)+3z_(2)-4z_(3)=0 then z_(1),z_(2),z_(3) are

If z_1 = cos theta + i sin theta and 1,z_1,(z_1)^2,(z_1)^3,.....,(z_1)^(n-1) are vertices of a regular polygon such that (Im(z_1)^2)/(Re Z_1) = (sqrt5-1)/2 , then the value n is

If the complex numbers z_(1), z_(2), z_(3) represent the vertices of an equilateral triangle, and |z_(1)|= |z_(2)| = |z_(3)| , prove that z_(1)+ z_(2) + z_(3)=0

If z_(1),z_(2),z_(3),…………..,z_(n) are n nth roots of unity, then for k=1,2,,………,n

If z_(1),z_(2),z_(3),…………..,z_(n) are n nth roots of unity, then for k=1,2,,………,n

If z_(1),z_(2),z_(3),…………..,z_(n) are n nth roots of unity, then for k=1,2,,………,n

If z_(1),z_(2),z_(3),…………..,z_(n) are n nth roots of unity, then for k=1,2,,………,n

If z_(1) + z_(2) + z_(3) = 0 and |z_(1)| = |z_(2)| = |z_(3)| = 1 , then value of z_(1)^(2) + z_(2)^(2) + z_(3)^(2) equals

If |z_(1)|=|z_(2)|=|z_(3)| and z_(1)+z_(2)+z_(3)=0 , then z_(1),z_(2),z_(3) are vertices of