1
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
2
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
$$- i{z_1} + (1 + i){z_2}$$
3
WB JEE 2023
+1
-0.25

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
$${a \over z} + {{\overline a } \over z} = 0$$
4
WB JEE 2022
+1
-0.25

If $$|z - 25i| \le 15$$, then Maximum arg(z) $$-$$ Minimum arg(z) is equal to

(arg z is the principal value of argument of z)

A
$$2{\cos ^{ - 1}}\left( {{3 \over 5}} \right)$$
B
$$2{\cos ^{ - 1}}\left( {{4 \over 5}} \right)$$
C
$${\pi \over 2} + {\cos ^{ - 1}}\left( {{3 \over 5}} \right)$$
D
$${\sin ^{ - 1}}\left( {{3 \over 5}} \right) - {\cos ^{ - 1}}\left( {{3 \over 5}} \right)$$
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