Let , where S_1 = z C : |z| 0 and . Find the area of…

MATHEMATICS · Single correct · CBSE · Mathematics · Complex Numbers and Quadratic Equations · Complex Numbers and Quadratic Equations

Problem

Let

S = S_1 \cap S_2 \cap S_3

, where

S_1 = \{z \in C : |z| < 4\},

S_2 = \left\{ z \in C : \operatorname{Im} \left[ \frac{z - 1 + \sqrt{3}i}{1 - \sqrt{3}i} \right] > 0 \right\}

and

S_3 = \{z \in C : \operatorname{Re} z > 0\}

. Find the area of

S

. (1)

\frac{10\pi}{3}

(2)

\frac{20\pi}{3}

(3)

\frac{16\pi}{3}

(4)

\frac{32\pi}{3}