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:

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: (A) √17 (B) 2√2 (C) (3/2)√2 (D) (5/2)√2

Tardigrade Admin · Accepted Answer

R1= w ∈ C:|ω-(4+i)| ≤ r ; R2= z ∈ C:|z-1| ≤| z+i| <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/6509cb3eb823f753e7eedf0a23624de3-.png" /> ∴ largest 'r'=C P=(|4+1|/√(1)2+(1)2)=(5/2)=(5 √2/2)

Q. The largest value of $r$ for which the region represented by the set ${ω \in C /∣ ω - 4 - i ∣ \leq r}$ is contained in the region represented by the set ${z \in C /∣ z - 1∣ \leq ∣ z + i ∣}$ , is equal to:

$17$

$22$

$\frac{3}{2} 2$

$\frac{5}{2} 2$

$R_{1} = {w \in C : ∣ ω - (4 + i) ∣ \leq r}; R_{2} = {z \in C : ∣ z - 1∣ \leq ∣ z + i ∣}$

$∴$ largest $^{'} r^{'} = CP = \frac{∣4 + 1∣}{( 1 ) ^{2} + ( 1 ) ^{2}} = \frac{5}{2} = \frac{5 2}{2}$

Q. 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:

17​

22​

23​2​

25​2​