For n N, let S_n= \z C: |z-3+2i |= n4 \ and T_n= \z C: |z-2+3i |= 1n \. Then the number of elements in the set
N: S_n T_n= \ is:

Question

For n N, let S_n= \z C: |z-3+2i |= n4 \ and T_n= \z C: |z-2+3i |= 1n \. Then the number of elements in the set 
 N: S_n T_n= \ is:

Accepted Answer

Correct answer: D. (d) S_n : |z - (3 - 2i)| = n4 is a circle center C_1(3,-2) and radius n/4 T_n : |z - (2 - 3i)| = 1n is a circle center C_2 (2,-3) and radius 1/n Here S_n T_n= Both circles do not intersect each other Case-1: C_1C_2 > n/4 + 1/n 2> n4+ 1n then n = 1, 2, 3, 4 Case-2: C_1C_2<( n4- 1n) 2< ( n^2-44n ) n has infinite solutions for n N

$For n \in N, let S_{n} = {z \in C : ∣ z - 3 + 2 i ∣ = \frac{n}{4}} and T_{n} = {z \in C : ∣ z - 2 + 3 i ∣ = \frac{1}{n}} . Then the number of elements in the set {n \in N : S_{n} \cap T_{n} = φ} is:$

Solution

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