WB JEE 2011 | Complex Numbers Question 15 | Mathematics

WB JEE 2011

MCQ (Single Correct Answer)

-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

$${{3n} \over {\omega - 1}}$$

$$3n(\omega - 1)$$

$${{\omega - 1} \over {3n}}$$

WB JEE 2023

MCQ (Single Correct Answer)

-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 $${z_3} = $$

$$ - i{z_1} - (1 + i){z_2}$$

$${z_1} - (1 + i){z_2}$$

$${z_1} + (1 + i){z_2}$$

$$ - i{z_1} + (1 + i){z_2}$$

WB JEE 2023

MCQ (Single Correct Answer)

-0.25

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

$$az + \overline {az} = 0$$

$$\overline a z - a\overline z = 0$$

$$az - \overline {az} = 0$$

$${a \over z} + {{\overline a } \over z} = 0$$

WB JEE 2022

MCQ (Single Correct Answer)

-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)

$$2{\cos ^{ - 1}}\left( {{3 \over 5}} \right)$$

$$2{\cos ^{ - 1}}\left( {{4 \over 5}} \right)$$

$${\pi \over 2} + {\cos ^{ - 1}}\left( {{3 \over 5}} \right)$$

$${\sin ^{ - 1}}\left( {{3 \over 5}} \right) - {\cos ^{ - 1}}\left( {{3 \over 5}} \right)$$

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