for any complex nuber z maximum value of `|z|-|z-1|` is (A) 0 (B) `1/2` (C) 1 (D) `3/2`

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

The minimum value of |z|+|z-1|+|z-2|is(A)0(B)1(C)2(D)4

For all complex numbers z_1,z_2 satisfying |z_1|=12 and |z_2-3-4i|=5 the minimum value of |z_1-z_2| is (A) 0 (B) 2 (C) 7 (D) 17

Number of imaginary complex numbers satisfying the equation, z^2=bar(z)2^(1-|z|) is (A) 0 (B) 1 (C) 2 (D) 3

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) are two non-zero complex numbers, then the maximum value of (Z_(1)bar(Z)_(2)+Z_(2)bar(Z)_(1))/(2|Z_(1)||Z_(2)|) is

Find the complex number z with maximum and minimum possible values of |z| satisfying (a) |z + (1)/(z) | =1 . (b) |z+ (4)/(z)| =3 .