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Complex Numbers question

2013 · Shift 2 · Q37

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PYQ Library
JEE Advanced
Mathematics
Complex Numbers
2013 · Shift 2 · Q37

Complex Numbers question

2013 · Shift 2 · Q37

JEE AdvancedMathematicsComplex NumbersMCQ+4 / −1

Let

S = S_1 \cap S_2 \cap S_3

, where

S_1 = \{z \in \mathbb{C} : |z| \lt 4\}, \quad S_2 = \left\{z \in \mathbb{C} : \text{Im}\left[\frac{z - 1 + \sqrt{3}i}{1 - \sqrt{3}i}\right] \gt 0\right\}

and

S_3 = \{z \in \mathbb{C} : \text{Re}(z) \gt 0\}

Area of

S

=

A
${{10\pi } \over 3}$
B
${{20\pi } \over 3}$
C
${{16\pi } \over 3}$
D
${{32\pi } \over 3}$

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