Set, Relation and FunctionEasy
Question
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 :
Options
A.3/2 √2
B.
C.2√2
D.5/2√2
Solution
|ω - 4 - i| ≤ r ⇒ circle centre (4, 1) radius = r
|z - 1| ≤ |z + i| ⇒ straight line y = - x
∴ maximum r =
|z - 1| ≤ |z + i| ⇒ straight line y = - x
∴ maximum r =
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