A (z₁=2+2 i ), B (z₂ ), C (z₃ ) are three points on the Argand plane satisfying |z_k-2 i |=2,(k=1,2,3) . If A B C encloses the maximum area, then the sum of the imaginary parts of z₂ and z₃ is

Step-by-step solution

According to given information |z-2 i|=2 is a circle having centre is (0,2) and radius is 2 . If the area of A B C is maximum the triangle must be equilateral triangle and point M is the mid point of B C , where M is the foot of perpendicular of point A (z₁=2+2 i ) on B C . Sum of the imaginary parts of z₂ and z₃ is twice of the imaginary part of M=2 2=4 .