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Complex Numbers question

2022 · 26 Jun · Shift 1 · Q22

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PYQ Library
JEE Main
Mathematics
Complex Numbers
2022 · 26 Jun · Shift 1 · Q22

Complex Numbers question

2022 · 26 Jun · Shift 1 · Q22

JEE MainMathematicsComplex NumbersMCQ+4 / −1

Let

A = \left\{ {z \in C:\left| {{{z + 1} \over {z - 1}}} \right| \lt 1} \right\}

and

B = \left\{ {z \in C:\arg \left( {{{z - 1} \over {z + 1}}} \right) = {{2\pi } \over 3}} \right\}

. Then A

\cap

B is :

A
a portion of a circle centred at $\left( {0, - {1 \over {\sqrt 3 }}} \right)$ that lies in the second and third quadrants only
B
a portion of a circle centred at $\left( {0, - {1 \over {\sqrt 3 }}} \right)$ that lies in the second quadrant only
C
an empty
D
a portion of a circle of radius ${2 \over {\sqrt 3 }}$ that lies in the third quadrant only

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