List of top Mathematics Questions on Complex Numbers and Quadratic Equations asked in WBJEE JENPAS UG

If \( \cos(\theta+\phi)=\frac{3}{5} \) and \( \sin(\theta-\phi)=\frac{5}{13} \), \( 0<\theta,\phi<\frac{\pi}{4} \), then \( \cot(2\theta) \) equals:
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:
Let \( \omega (\ne 1) \) be a cube root of unity. Then the minimum value of the set \[ \left\{ |a + b\omega + c\omega^2|^2 : a,b,c \text{ are distinct non-zero integers} \right\} \] equals:
If \( z_1, z_2 \) are complex numbers such that \( \dfrac{2z_1}{3z_2} \) is a purely imaginary number, then the value of \[ \left|\frac{z_1 - z_2}{z_1 + z_2}\right| \] is: