Let `z_k` be the roots of the equation `(z+1)^7+z^7=0`, then `sum _(k=0)^6 Re(z_k)` is `-k/2`, then `k` is-------------

If z_(r)(r=0,1,2,…………,6) be the roots of the equation (z+1)^(7)+z^7=0 , then sum_(r=0)^(6)"Re"(z_(r))=

If z_(r)(r=0,1,2,…………,6) be the roots of the equation (z+1)^(7)+z^7=0 , then sum_(r=0)^(6)"Re"(z_(r))=

If z_(1) and z_(2) satisfy the equation |z-2|=|"Re"(z)| and arg (z1-z2)=pi/3, then Im (z1+z2) =k/sqrt 3 where k 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

Let z be a non - real complex number which satisfies the equation z^(23) = 1 . Then the value of sum_(22)^(k = 1 ) (1)/(1 + z ^( 8k) + z ^( 16k ))

Let z be a non - real complex number which satisfies the equation z^(23) = 1 . Then the value of sum_(22)^(k = 1 ) (1)/(1 + z ^( 8k) + z ^( 16k ))

If z_(k)=e^(i theta_k) for k= 1, 2, 3, 4 where i^(2)= -1 , and if |sum_(k=1)^(4) (1)/(z_k)|=1 , then |sum_(k=1)^(4)| is equal to

If z-(1)/(z)=i then z^(2005)+(1)/(z^(2005))=+-sqrt(k) then k is

The locus of the point z satisfying Re(1/z) = k , where k is non -zero real number , is :