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Complex Numbers question

2024 · 5 Apr · Shift 2 · Q35

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PYQ Library
JEE Main
Mathematics
Complex Numbers
2024 · 5 Apr · Shift 2 · Q35

Complex Numbers question

2024 · 5 Apr · Shift 2 · Q35

JEE MainMathematicsComplex NumbersMCQ+4 / −1

Let

S_1=\{z \in \mathbf{C}:|z| \leq 5\}, S_2=\left\{z \in \mathbf{C}: \operatorname{Im}\left(\frac{z+1-\sqrt{3} i}{1-\sqrt{3} i}\right) \geq 0\right\}

and

S_3=\{z \in \mathbf{C}: \operatorname{Re}(z) \geq 0\}

. Then the area of the region

S_1 \cap S_2 \cap S_3

is :

A
$\frac{125 \pi}{24}$
B
$\frac{125 \pi}{6}$
C
$\frac{125 \pi}{12}$
D
$\frac{125 \pi}{4}$

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