1
WB JEE 2011
+1
-0.25

If $$\omega$$ $$\ne$$ 1 is a cube root of unity, then the sum of the series $$S = 1 + 2\omega + 3{\omega ^2} + \,\,.....\,\, + 3n{\omega ^{3n - 1}}$$ is

A
$${{3n} \over {\omega - 1}}$$
B
$$3n(\omega - 1)$$
C
$${{\omega - 1} \over {3n}}$$
D
0
2
WB JEE 2024
+1
-0.25

If $$z_1$$ and $$z_2$$ be two roots of the equation $$z^2+a z+b=0, a^2<4 b$$, then the origin, $$\mathrm{z}_1$$ and $$\mathrm{z}_2$$ form an equilateral triangle if

A
$$\mathrm{a}^2=3 \mathrm{b}^2$$
B
$$\mathrm{a^2=3 b}$$
C
$$\mathrm{b}^2=3 \mathrm{a}$$
D
$$\mathrm{b}^2=3 \mathrm{a}^2$$
3
WB JEE 2024
+1
-0.25

If $$\cos \theta+i \sin \theta, \theta \in \mathbb{R}$$, is a root of the equation

$$a_0 x^n+a_1 x^{n-1}+\ldots .+a_{n-1} x+a_n=0, a_0, a_1, \ldots . a_n \in \mathbb{R}, a_0 \neq 0,$$

then the value of $$a_1 \sin \theta+a_2 \sin 2 \theta+\ldots .+a_n \sin n \theta$$ is

A
2n
B
n
C
0
D
n + 1
4
WB JEE 2023
+1
-0.25

If the vertices of a square are $${z_1},{z_2},{z_3}$$ and $${z_4}$$ taken in the anti-clockwise order, then $${z_3} =$$

A
$$- i{z_1} - (1 + i){z_2}$$
B
$${z_1} - (1 + i){z_2}$$
C
$${z_1} + (1 + i){z_2}$$
D
$$- i{z_1} + (1 + i){z_2}$$
EXAM MAP
Medical
NEET