If `z^(2)+z+1=0`, where z is a complex number, the value of `(z+1/z)^(2)+(z^(2)+1/z^(2))^(2)+(z^(3)+1/z^(3))^(2)+...+(z^(6)+1/z^(6))^(2)` is

If z^2+z+1=0 where z is a complex number, then the value of (z+1/z)^2+(z^2+1/z^2)^2+....+(z^6+1/z^6)^2 is

For any two complex numbers z_(1),z_(2) the values of |z_(1)+z_(2)|^(2)+|z_(1)-z_(2)|^(2) , is

For any two complex numbers z_(1) and z_(2) |z_(1)+z_(2)|^(2) =(|z_(1)|^(2)+|z_(2)|^(2))

If z_(1),z_(2) and z_(3) be unimodular complex numbers, then the maximum value of |z_(1)-z_(2)|^(2)+|z_(2)-z_(3)|^(2)+|z_(3)-z_(1)|^(2) , is

If z_(1),z_(2),z_(3) are three complex numbers, such that |z_(1)|=|z_(2)|=|z_(3)|=1 & z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=0 then |z_(1)^(3)+z_(2)^(3)+z_(3)^(3)| is equal to _______. (not equal to 1)

If z_(1) and z_(2) are two complex numbers such that |(z_(1)-z_(2))/(z_(1)+z_(2))|=1 , then

For complex number z,|z-1|+|z+1|=2, then z lies on

z is a complex number satisfying z^(4)+z^(3)+2z^(2)+z+1=0 , then |z| is equal to

If z_1,z_2 are two complex numbers such that Im(z_1+z_2)=0,Im(z_1z_2)=0 , then:

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