If `|z| <= 1 and |omega| <= 1,` show that `|z-omega|^2 <= (|z|-|omega|)^2+(arg z-arg omega)^2`

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 _____.

If |z_1|=|z_2|=.......=|z_n|=1, prove that |z_1+z_2+z_3++z_n|=1/(z_1)+1/(z_2)+1/(z_3)++1/(z_n)

If |z_1|=|z_2|=|z_3|=......=|z_n|=1 , then |z_1+z_2+z_3+......+z_n|=

If |z_1|=|z_2|=1, then prove that |z_1+z_2| = |1/z_1+1/z_2∣

If |z_1|=1, |z_2|=2, |z_3|=3 and |9z_1z_2 + 4z_1z_3 + z_2z_3|=36 , then |z_1+z_2+z_3| is equal to _______.

If |z_1|=2, |z_2|=3, |z_3|=4 and |2z_1+3z_2 + 4z_3|=9 , then value of |8z_2z_3 + 27z_3z_1 + 64z_1z_2|^(1//3) is :

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

If |z-3|=min{|z-1|,|z-5|} , then Re(z) equals to

, a point 'z' is equidistant from three distinct points z_(1),z_(2) and z_(3) in the Argand plane. If z,z_(1) and z_(2) are collinear, then arg (z(z_(3)-z_(1))/(z_(3)-z_(2))). Will be (z_(1),z_(2),z_(3)) are in anticlockwise sense).

Let z_(1),z_(2),z_(3),z_(4) are distinct complex numbers satisfying |z|=1 and 4z_(3) = 3(z_(1) + z_(2)) , then |z_(1) - z_(2)| is equal to