If `z and bar z` represent adjacent vertices of a regular polygon of `n` sides where centre is origin and if `(Im(z))/(Re(z)) = sqrt(2) - 1`, then `n` is equal to:

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 z=-2+2sqrt(3)i, then z^(2n)+2^(2n)*z^n+2^(4n) is equal to

Let z be a complex number such that |z|+z=3+I (Where i=sqrt(-1)) Then ,|z| is equal to

The center of a regular polygon of n sides is located at the point z=0, and one of its vertex z_(1) is known. If z_(2) be the vertex adjacent to z_(1) , then z_(2) is equal to _____________.

If (3+i)(z+bar(z))-(2+i)(z-bar(z))+14i=0 , where i=sqrt(-1) , then z bar(z) is equal to

If z^4+1=sqrt(3)i (A) z^3 is purely real (B) z represents the vertices of a square of side 2^(1/4) (C) z^9 is purely imaginary (D) z represents the vertices of a square of side 2^(3/4)

If z_1 and z_2 are complex numbers such that |z_1-z_2|=|z_1+z_2| and A and B re the points representing z_1 and z_2 then the orthocentre of /_\OAB, where O is the origin is (A) (z_1+z_2)/2 (B) 0 (C) (z_1-z_2)/2 (D) none of these

If z_(1),z_(2),z_(3)………….z_(n) are in G.P with first term as unity such that z_(1)+z_(2)+z_(3)+…+z_(n)=0 . Now if z_(1),z_(2),z_(3)……..z_(n) represents the vertices of n -polygon, then the distance between incentre and circumcentre of the polygon is

Re((z+4)/(2z-1)) = 1/2 , then z is represented by a point lying on

Number of solutions of Re(z^(2))=0 and |Z|=a sqrt(2) , where z is a complex number and a gt 0 , is