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

The region represented by the set ω ∈ C ||ω - i|| ≤ r is a circular region whose center is (0, 1) (x²)² + (y²)² ≤ r² ———(1)
And the region represented by the set z ∈ C ||z|| ≤ |z + i| is
(x²)² + y² ≤ x² + (y + 1)² ⇒ 0 ≤ 2y + 1 ⇒ x + y ≥ 0 ———(2)
Limiting condition is x + y = 0 is tangent to the circle (x²)² + (y²)² = r² ⇒ 4 + 1 √2 = r ⇒ r = 5√2/2
∴ Largest value of r is 5√2
Hence, option C.