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Complex Numbers question

2008 · Shift 1 · Q35

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PYQ Library
JEE Advanced
Mathematics
Complex Numbers
2008 · Shift 1 · Q35

Complex Numbers question

2008 · Shift 1 · Q35

JEE AdvancedMathematicsComplex NumbersMCQ+3 / −1

Let A, B, C be three sets of complex numbers as defined below

A = \left\{ {z:\,{\mathop{\rm Im} olimits} \,\,z\,\, \ge \,1} \right\}B = \left\{ {z:\,\,\left| {z - 2 - i} \right| = 3} \right\}C = \left\{ {z:\,{\mathop{\rm Re} olimits} (1 - i)z) = \sqrt 2 \,} \right\}

Let z be any point

A \cap B \cap C

and let w be any point satisfying

\left| {w - 2 - i} \right| \lt 3\,

. Then,

\left| z \right| - \left| w \right| + 3

lies between :

A
- 6 and 3
B
- 3 and 6
C
- 6 and 6
D
- 3 and 9

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