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 = (1)/(1 - cos theta - i sin theta), the Re (z)=

Let A(z_1),A_2(barz_1) are the adjacent vertices of a regular polygon if (Im(barz_1))/(Re(z_1))=1-sqrt2 then number of sides of the polygon is equal to

If z_(1) and overline(z)_(1) represent adjacent vertices of a regular polygon of n sides whose centre is origin and if (Im (z_(1)) )/(Re (z_(1))) = sqrt(2)-1 then n is equal to:

If z_1& z_1 represent adjacent vertices of a regular polygon on n sides with centre at the origin & if (l m(z_1))/(R e(z_1))=sqrt(2)-1 then the value of n is equal to: 8 (b) 12 (c) 16 (d) 24

If z_1 = 1-i and z_2 = 2+4i , then im[frac{z_1z_2}{z_1} =

If 1,z_1 ​ ,z_2 ​ ,z_3 ​ ,...,z_(n−1) ​ are nth roots of unity, then show that (1−z_1 ​ )(1−z_2 ​ )...(1−z_(n−1) ​ )=n

If z_1 and bar z_1 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 n is an integer and z=cos theta+i sin theta , then (z^(2 n)-1)/(z^(2 n)+1)=