The largest value of r , for which the region represented by the set ω ∈ C ω - 4 - i ≤ r is contained in the region represented by the set z ∈ C z - 1 ≤ z + i , is equal to :

Step-by-step solution

z - 1 ≤ z + i Putting z = x + i y and simplifying, we get x + y ≥ 0 The region in shown shaded right side of the line x + y = 0 The largest value of r would be the length of perpendicular from A 4 , 1 , on the line x + y = 0 4 + 1 2 =   5 2 =   5 2 2