If `z+1/z=1` and `z` be any complex number,then the value of `z^(99)+(1)/(z^(99))` 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

If z is a complex number, then the minimum value of |z|+|z-1| is -

For any complex number z, the minimum value of |z|+|z-1|

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

Let z, be a complex number with |z_(1)|=1 and z_(2) be any complex number,then |(z_(1)-z_(2))/(1-z_(1)z_(2))|=

If arg(z_(2)-z_(1))+arg(z_(3)-z_(1))=2arg(z-z_(1)) where z,z_(1),z_(2) and z_(3) ,are complex numbers, then the locus of z is