Let A = { z : 1 | z - ( 1 + i ) | 2 } and B = { z A : | z - ( 1 - i ) | = 1 } . Then B:

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Solution

Q.
Let $A = {z \in ℂ : 1 \leq | z - (1 + i) | \leq 2}$ and $B = {z \in A : | z - (1 - i) | = 1}$ . Then B:

1 is an empty set

2 contains exactly two elements

3 contains exactly three elements

4 is an infinite set

Ans.
(4)

$A = {z \in C : 1 \leq | z - (1 + i) | \leq 2}$

$B = {z \in A : | z - (1 - i) | = 1}$ $A \cap B has infinite set.$

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