If `z=1-i` find the value of `z^(6)-z^(4)+z^(2)-1`

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

1.If Z=(1+i)/(sqrt(2)) find the value of Z^(6)+Z^(4)+Z^(2) .

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

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

If |z_(1)|=1,|z_(2)|=2,|z_(3)|=3, and |9z_(1)z_(2)+4z_(1)z_(3)+z_(2)z_(3)|=12 then find the value of |z_(1)+z_(2)+z_(3)|

If z = i(i + sqrt(2)) , then value of z^(4) + 4z^(3) + 6z^(2) + 4z is

If z_(1),z_(2) and z_(3),z_(4) are two pairs of conjugate complex numbers,hen find the value of arg(z_(1)/z_(4))+arg(z_(2)/z_(3))*a

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

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