The common roots of the equation `Z^3+2Z^2+2Z+1=0` and `Z^1985+Z^100+1=0` are

Sum of common roots of the equations z^(3) + 2z^(2) + 2z + 1 =0 and z^(1985) + z^(100) + 1=0 is

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

If z_(1) and z_(2) are the complex roots of the equation (x-3)^(3) + 1=0 , then z_(1) +z_(2) equal to

Prove that quadrilateral formed by the complex numbers which are roots of the equation z^(4) - z^(3) + 2z^(2) - z + 1 = 0 is an equailateral trapezium.

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 :

If one root of the equation z^2-a z+a-1= 0 is (1+i), where a is a complex number then find the root.

If z_1,z_2,z_3,………..z_(n-1) are the roots of the equation 1+z+z^2+…….+z^(n-1)=0, where n epsilon N, ngt2 then (A) z_1,z_2, …z_(n-1) are terms of a G.P. (B) z_1,z_2,……,z_(n-1) are terms of an A.P. (C) |z_1|=|z_2|=|z_3|=.|z_(n-1)|!=1 (D) none of these

If z_(1),z_(2),z_(3),…,z_(n-1) are the roots of the equation z^(n-1)+z^(n-2)+z^(n-3)+…+z+1=0 , where n in N, n gt 2 and omega is the cube root of unity, then

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 :

The number of values of z (real or complex) e simultaneously satisfying the system of equations 1+z+z^2+z^3+...z^17=0 and 1+z+z^2+z^3+..+z^13=0 is