If `z=1/2(isqrt3-1),`then find the value of `(z-z^2+2z^3)(2-z+z^2)`

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 2z_1//3z_2 is a purely imaginary number, then find the value of "|"(z_1-z_2")"//(z_1+z_2)|dot

If 2z_1//3z_2 is a purely imaginary number, then find the value of "|"(z_1-z_2")"//(z_1+z_2)|dot

If 2z_1//3z_2 is a purely imaginary number, then find the value of "|"(z_1-z_2")"//(z_1+z_2)|dot

If z^(2)+(1)/(z^(2))=14, find the value of z^(3)+(1)/(z^(3))

if z^2+z+1=0 , then the value of (z+1/z)^2+(z^2+1/z^2)^2+(z^3+1/z^3)^2+......+(z^21+1/z^21)^2 is

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

If z_(1),z_(2),z_(3) satisfy the system of equations given by |z_(1)|=|z_(2)|=|z+3|=1,z_(1)+z_(2)+z_(3)=1 and z_(1)z_(2)z_(3)=1 such that lm(z_(1))

If |z_1|=1,|z_2|=2,|z_3|=3,a n d|9z_1z_2+4z_1z_3+z_2z_3|=12 , then find the value of |z_1+z_2+z_3|dot