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Complex Numbers question

2025 · 8 Apr · Shift 2 · Q35

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JEE Main
Mathematics
Complex Numbers
2025 · 8 Apr · Shift 2 · Q35

Complex Numbers question

2025 · 8 Apr · Shift 2 · Q35

JEE MainMathematicsComplex NumbersMCQ+4 / −1

Let

A = \left\{ \theta \in [0, 2\pi] : 1 + 10\operatorname{Re}\left( \frac{2\cos\theta + i\sin\theta}{\cos\theta - 3i\sin\theta} \right) = 0 \right\}

. Then

\sum\limits_{\theta \in A} \theta^2

is equal to

A
$\frac{21}{4} \pi^2$
B
$6\pi^2$
C
$\frac{27}{4} \pi^2$
D
$8\pi^2$

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