Question

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

• A. $\sqrt{17}$
• B. $2\sqrt{2}$
• C. $\frac{3}{2}\sqrt{2}$
• D. $\frac{5}{2}\sqrt{2}$

Answer 1

Answer: (D)

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

$\therefore $ largest $'r'=C P=\frac{|4+1|}{\sqrt{(1)^{2}+(1)^{2}}}=\frac{5}{2}=\frac{5 \sqrt{2}}{2}$