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

If z_(1) and z_(2) are two complex numbers such that |z_(1)|= |z_(2)| , then is it necessary that z_(1) = z_(2)

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

If |(z-z_(1))//(z-z_(2))| = 3 , where z_(1) and z_(2) are fixed complex numbers and z is a variable complex complex number, then z lies on a

The number of complex numbers z such that |z-1|=|z+1|=|z-i| 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 satisfying z + z^-1 = 1 then z^n + z^-n , n in N , has the value

For a complex number Z,|Z|=1 and "arg "(Z)=theta . If (Z)(Z^(2))(Z^(3))…(Z^(n))=1 , then the value of theta is

If z_1 and z_2 are two complex numbers such that |z_1|lt1lt|z_2| then prove that |(1-z_1barz_2)/(z_1-z_2)|lt1

Let z_1,z_2 be complex numbers with |z_1|=|z_2|=1 prove that |z_1+1| +|z_2+1| +|z_1 z_2+1| geq2 .

For two complex numbers z_(1) and z_(2) , we have |(z_(1)-z_(2))/(1-barz_(1)z_(2))|=1 , then