If `z` is a nonreal root of `root(7)(-1)` , then find the value of `z^(86)+z^(175)+z^(289)dot`

If z is nonreal root of [-1]^((1)/(7)) then,find the value of z^(86)+z^(175)+z^(289)

If z + z^(-1)= 1 , then find the value of z^(100) + z^(-100) .

If z=4+i sqrt(7), then find the value of z^(2)-4z^(2)-9z+91

if |z|=1, then find the value of (1+z)/(1-z) .

If z=(1)/(2)(i sqrt(3)-1), then find the value of (z-z^(2)+2z^(3))(2-z+z^(2))

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 2z_(1)/3z_(2) is a purely imaginary number,then find the value of |(z_(1)-z_(2))/(z_(1)+z_(2))|

If z_(r):r=1,2,3,,50 are the roots of the equation sum_(r=0)^(50)z^(r)=0, then find the value of sum_(r=0)^(50)(1)/(z_(r)-1)

If a_(1),a_(2),a_(3) are the roots of z^(3)-3z^(2)+3z+7=0, then find the value of |sum_(i!=j)((a_(i)-1)/(a_(j)-1))|

If arg((z_(1))/(z_(2)))=(pi)/(2), then find the value of |(z_(1)+z_(2))/(z_(1)-z_(2))|