Let $A , B , C$ be three sets of complex numbers as defined below $$\begin{aligned} & A = \{ z : \operatorname { Im } z \geq 1 \} \\ & B = \{ z : | z - 2 - i | = 3 \} \\ & C = \{ z : \operatorname { Re } ( ( 1 - i ) z ) = \sqrt { 2 } \} \end{aligned}$$ Let $z$ be any point in $A \cap B \cap C$ and let $w$ be any point satisfying $| w - 2 - i | < 3$. Then, $| z | - | w | + 3$ lies between
(A) -6 and 3
(B) - 3 and 6
(C) - 6 and 6
(D) - 3 and 9
Let $A , B , C$ be three sets of complex numbers as defined below
$$\begin{aligned}
& A = \{ z : \operatorname { Im } z \geq 1 \} \\
& B = \{ z : | z - 2 - i | = 3 \} \\
& C = \{ z : \operatorname { Re } ( ( 1 - i ) z ) = \sqrt { 2 } \}
\end{aligned}$$
Let $z$ be any point in $A \cap B \cap C$ and let $w$ be any point satisfying $| w - 2 - i | < 3$. Then, $| z | - | w | + 3$ lies between\\
(A) -6 and 3\\
(B) - 3 and 6\\
(C) - 6 and 6\\
(D) - 3 and 9