If `z=re^(itheta)` ( r gt 0 & `0 le theta lt 2pi`) is a root of the equation `z^8-z^7+z^6-z^5+z^4-z^3+z^2 -z + 1=0` then number of value of `'theta'` is :

Let Z=re^(itheta)(r gt 0 and pi lt theta lt 3pi) is a root of the equation Z^(8)-Z^(7)+Z^(6)-Z^(5)+Z^(4)-Z^(3)+Z^(2)-Z+1=0 . the sum of all values of theta is kpi . Then k is equal to

The equation z^5+z^4+z^3+z^2+z+1 =0 is satisfied by

If |z-i|=1 and arg (z) =theta where 0 lt theta lt pi/2 , then cottheta-2/z equals

let z_1,z_2,z_3 and z_4 be the roots of the equation z^4 + z^3 +2=0 , then the value of prod_(r=1)^(4) (2z_r+1) is equal to :

The complex number z has argZ = theta , 0 lt theta lt (pi)/(2) and satisfy the equation |z-3i|=3 . Then value of ( cot theta-(6)/(z)) =

Common roots of the equation z^(3)+2z^(2)+2z+1=0 and z^(2020)+z^(2018)+1=0 , are

If z is a complex number satisfying z^(4)+z^(3)+2z^(2)+z+1=0 then the set of possible values of z is