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Complex Numbers question

2013 · Shift 2 · Q22

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PYQ Library
JEE Advanced
Mathematics
Complex Numbers
2013 · Shift 2 · Q22

Complex Numbers question

2013 · Shift 2 · Q22

JEE AdvancedMathematicsComplex NumbersMultiple correct+4 / −1

Let

\omega=\frac{\sqrt{3}+i}{2}

and

P=\left\{\omega^n: n=1,2,3, \ldots\right\}

. Further

\mathrm{H}_1=\left\{z \in \mathrm{C}: \operatorname{Re} z\lt \frac{1}{2}\right\}

and

\mathrm{H}_2=\left\{z \in \mathrm{C}: \operatorname{Re} z\lt \frac{-1}{2}\right\}

, where C is the set of all complex numbers. If

z_1 \in \mathrm{P} \cap \mathrm{H}_1, z_2 \in\mathrm{P} \cap \mathrm{H}_2

and O represents the origin, then

\angle z_1 \mathrm{O} z_2=

A
${\pi \over 2}$
B
${\pi \over 6}\,$
C
${{2\pi } \over 3}$
D
${{5\pi } \over 6}$

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