Let ‘z’ be a complex number satisfying z-2-i≤5, Then z-14-6i lies in

|z−14−6i|=|(z−2−i)−(12+5i)|≤|z−2−i|+|12+5i|⇒ |z−14−6i|≤5+13=18|z−14−6i|max=CP+r=13+5=18|z−14−6i|min=CP−r=13−5=8

Let ‘z’ be a complex number satisfying z-2-i≤5, Then z-14-6i lies in

|z−14−6i|=|(z−2−i)−(12+5i)|≤|z−2−i|+|12+5i|⇒ |z−14−6i|≤5+13=18|z−14−6i|max=CP+r=13+5=18|z−14−6i|min=CP−r=13−5=8

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Let ‘z’ be a complex number satisfying $|z - 2 - i| \leq 5$ , Then $|z - 14 - 6 i|$ lies in

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[3, 7]

[0, 2]

[8, 18]

(2, 8)

answer is A.

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Detailed Solution

$| z - 14 - 6 i | = | (z - 2 - i) - (12 + 5 i) | \leq | z - 2 - i | + | 12 + 5 i |$

$\Rightarrow | z - 14 - 6 i | \leq 5 + 13 = 18$

$\begin{aligned} | z - 14 - 6 i |_{max} = C P + r \\ = 13 + 5 = 18 \end{aligned}$

$\begin{aligned} | z - 14 - 6 i |_{min} = C P - r \\ = 13 - 5 = 8 \end{aligned}$

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Let ‘z’ be a complex number satisfying $|z - 2 - i| \leq 5$ , Then $|z - 14 - 6 i|$ lies in