jee-main 2022 Q62

jee-main · India · session1_24jun_shift1 Complex Numbers Argand & Loci Intersection of Loci and Simultaneous Geometric Conditions

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

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

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