Mathematics

Mathematics

Problem

Let

A

,

B

and

C

be three sets of complex numbers as defined below:

A = \{z : \operatorname{Im}(z) \ge 1\}

B = \{z : |z - 2 - i| = 3\}

C = \{z : \operatorname{Re}((1 - i)z) = \sqrt{2}\}, \text{ where } i = \sqrt{-1}

Let

z

be any point in

A \cap B \cap C

and

\omega

be any point satisfying

|\omega - 2 - i| < 3

. Then,

|z| - |\omega| + 3

lies between a.

-6

and

3

b.

-3

and

6

c.

-6

and

6

d.

-3

and

9

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