`|(Z_1 - 1)/(Z_1 - 4)| = 2 & | (Z_2 - 4)/ (Z_2 - 1)| = 2` the `|Z_1 - Z_2|_max - |Z_1 + Z_1|_min` = ?

(Z_ (1) -1) / (Z_ (1) -4) | = 2 & | (Z_ (2) -4) / (Z_ (2) -1) | = 2 the Z_ (1) -Z_ (2 ) | _ (max) - | Z_ (1) + Z_ (1) | _ (min) =?

If Z_1 = -3 + 4i , Z_2 = 12 - 5i , prove that |z_1+z_2|<|z_1-z_2|

If |z_1|=|z_2|=1 , then |z_1+z_2| =

If z_1 = 4 - 7i , z_2 = 2 + 3i and z_3 = 1 + i show that z_1 + (z_2 + z_3) = (z_1 + z_2)+z_3

Minimum value of |z_1 + 1 | + |z_2 + 1 | + |z _1 z _2 + 1 | if [ z_1 | = 1 and |z_2 | = 1 is ________.

Minimum value of |z_1 + 1 | + |z_2 + 1 | + |z _1 z _2 + 1 | if [ z_1 | = 1 and |z_2 | = 1 is ________.

Let S={ Z in C : | z - 1|=1 and (sqrt 2 - 1) (z overline z) - i(z - overline z) = 2 sqrt 2} . Let z_1, z_2 be such that |z_1| = max_(z in S) |z| and |z_2| = min_(z in S) |z| . Then |sqrt2 z_1 - z_2|^2 equals:

If z_(1) satisfies |z-1|=1 and z_(2) satisfies |z-4i|=1 , then |z_(1)-z_(2)|_("max")-|z_(1)-z_(2)|_("min") is equal to ___________