Let Z be the non-real root of `x^(6)=1`, then `|Z^(5)+(1)/(Z^(5))|`=

If z is a non real cube root of unity, then (z+z^(2)+z^(3)+z^(4))^(9) is equal to

Let z be a root of x^(5)-1=0 with z!=1. The the value of z^(15)+z^(16)+z^(17)+.........+z^(50)

If 1,z_(1),z_(2),z_(3),......,z_(n-1) be the n, nth roots of unity and omega be a non-real complex cube root of unity,then prod_(r=1)^(n-1)(omega-z_(r)) can be equal to

If 1,z_(1),z_(2),z_(3).....z_(n-1) be n^(th) roots if unity and w be a non real complex cube root of unity, then prod_(r=1)^(n-1)(w-z_(r)) can be equal to

Find roots of the equation (z + 1)^(5) = (z - 1)^(5) .

Let alpha be the non-real 5 th root of unity. If z_1 and z_2 are two complex numbers lying on |z| = 2 , then the value of sum_(t=0) ^(4) |z_1 + alpha ^(t)z_2 |^(2) is ______ .

Let alpha and beta be real numbers and z be a complex number. If z^(2)+alphaz+beta=0 has two distinct non-real roots with Re(z)=1, then it is necessary that