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List of top Mathematics Questions on Complex numbers asked in WBJEE

If \( |z_1| = |z_2| = |z_3| = 1 \) and \( z_1 + z_2 + z_3 = 0 \), then the area of the triangle whose vertices are \( z_1, z_2, z_3 \) is:
If \( z_1, z_2 \) are complex numbers such that \( \frac{z_1}{3z_2} \) is a purely imaginary number, then the value of \( \left| \frac{z_1 - z_2}{z_1 + z_2} \right| \) is:
Let \( \omega (\neq 1) \) be a cubic root of unity. Then the minimum value of the set \( \{ |a + b\omega + c\omega^2|^2 : a, b, c \) are distinct non-zero integers \( \} \) equals:
If \(\cos\theta + i \sin\theta, \, \theta \in \mathbb{R}\), is a root of the equation
\[ a_0 x^n + a_1 x^{n-1} + \cdots + a_{n-1}x + a_n = 0, \, a_0, a_1, \ldots, a_n \in \mathbb{R}, \, a_0 \neq 0 \]
then the value of \(a_1 \sin\theta + a_2 \sin 2\theta + \cdots + a_n \sin n\theta\) is:
If \(z_1\) and \(z_2\) be two roots of the equation \(z^2 + az + b = 0, \, a^2 < 4b\), then the origin, \(z_1\) and \(z_2\) form an equilateral triangle if: