Let A, B, C be three sets of complex numbers as defined below. ` A = { z : |z+1| <= 2 + Re(z)}, B = { z : |z-1| >=1} and C = { z : |(z-1)/(z+1)|>=1}`

A,B,C be three sets of complex number as defined below : A = {z : "In" z ge 1} , B = {z :| z - 2 - I | = 3 } " and " C = {z : Re ((1 - i)z) = sqrt(2)) Let z be any point in A nn B nn C . The |z + 1 - i|^(2) + |z - 5 -i|^(2) lies between :

Let A,B,C be three sets of complex number as defined below A={z:lm (z) ge 1} B={z:|z-2-i|=3} C={z:Re((1-i)z)=sqrt(2)} Let z be any point in A cap B cap C and let w be any point satisfying |w-2-i|lt 3 Then |z|-|w|+3 lies between

Let A,B,C be three sets of complex number as defined below: A={z:Im>=1},B={z:|z-2-i|=3},C:{z:Re((1-i)z)=sqrt(2)} The number of elements in the set A nn B nn C is

Let z_1, z_2, z_3 be three distinct complex numbers satisfying |z_1 - 1| = |z_2-1| = |z_3-1| . Let A , B, and C be the points represented in the Argand plane corresponding to z_1 , z_2 and z_3 respectively. Prove that z_1 + z_2 + z_3=3 if and only if Delta ABC is an equilateral triangle.

Number of complex numbers such that |z| = 1 and z = 1 - 2 bar(z) is