1
WB JEE 2024
MCQ (Single Correct Answer)
+1
-0.25
Change Language

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
$$\mathrm{b}^2=3 \mathrm{a}^2$$
2
WB JEE 2024
MCQ (Single Correct Answer)
+1
-0.25
Change Language

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
3
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
Change Language

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
$$ - i{z_1} + (1 + i){z_2}$$
4
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
Change Language

Reflection of the line $$\overline a z + a\overline z = 0$$ in the real axis is given by :

A
$$az + \overline {az} = 0$$
B
$$\overline a z - a\overline z = 0$$
C
$$az - \overline {az} = 0$$
D
$${a \over z} + {{\overline a } \over z} = 0$$
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