z is a complex number such that `z+1/z=2cos 3^0` ,then the value of `z^(2000)+ 1/z^(2000)` is equal to

If z is a complex number such that |z|>=2 then the minimum value of |z+1/2| is

If z is a complex number such that |z|>=2 then the minimum value of |z+1/2| is

If z is a complex number such that |z|>=2 then the minimum value of |z+(1)/(2)| is

Let z=1+ ai be a complex number,a>0, such that z^(3) is a real number.Then the sum 1+z+z^(2)+...+z^(11) is equal to:

Let z=1+ai be a complex number, a > 0 ,such that z^3 is a real number. Then the sum 1+z+z^2+...+ z^11 is equal to:

For a complex number Z, if arg Z=(pi)/(4) and |Z+(1)/(Z)|=4 , then the value of ||Z|-(1)/(|Z|)| is equal to

For a complex number Z, if arg Z=(pi)/(4) and |Z+(1)/(Z)|=4 , then the value of ||Z|-(1)/(|Z|)| is equal to

If z is a complex number satisfying z^4+z^3+2z^2+z+1=0 then the set of possible values of z is