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| z1- z2| as z1& z2 over the curves √3

Let z_1, z_2 , z_3 in C such that |z_1 | = |z_2| = |z_3| = |z_1+ z_2+ z _3| = 4 . If |z_1 - z _2 | = | z _1 + z _ 3 | and z_2 ne z_3 , then values of |z_1 + z_2 |* |z_1 + z _ 3| is _____.

Find the minimum value of |z-1 if ||z-3|-|z+1||=2.

If z_(1) = 2 - i , z_(2) = 1 + i , " find " |(z_(1) + z_(2) + 1)/( z_(1) -z_(2) + 1)|

Find the minimum value of |z-1| if ||z-3|-|z+1||=2.

If |z_1 + z_2| = |z_1| + |z_2| is possible if :

If |z _1 |= 2 and (1 - i)z_2 + (1+i)barz_2 = 8sqrt2 , then the minimum value of |z_1 - z_2| is ______.

If z_1 , lies in |z-3|<=4,z_2 on |z-1|+|z+1|=3 and A = |z_1-z_2| , then :

Given that 1 + 2|z|^(2) = |z^(2) + 1|^(2) + 2 | z + 1 | ^(2) , then the value of |z(z + 1 )| is ______.

if z_(1) = 3i and z_(2) =1 + 2i , then find z_(1)z_(2) -z_(1)