JEE MATHEMATICS MCQ: COMPLEX NUMBERS

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Analyzing +4 | -1

{z_1},{z_2},{z_3}

be vertices of an equilateral triangle occurring in the anticlockwise sense, then

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Correct option: C

{z_1} + \omega \;{z_2} + {\omega ^2}{z_3} = 0

Option D (

- 2,\mathrm{ }2,\mathrm{ }4

) is correct because these are the solutions obtained by considering both positive and negative cases of the absolute value and verifying that they satisfy the original equation.

More Questions from COMPLEX NUMBERS

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The number of non-zero integer solutions of the equation

{\left| {1 - i} \right|^x} = {2^x}

is If

|z|=1

and

z \neq \pm 1

, then for any complex number

z, \frac{z}{1-z^2}

Let

\left|z_r-r\right| \leq r, \forall r=1,2,3, \ldots, n

, then

\left|\sum\limits_{r=1}^n z_r\right|

is less than The roots of the cubic equation

(z+a b)^3=a^3

, where

a \neq 0

represents the vertices of a triangle. If

\alpha, \beta

and

\gamma

are the roots, then find the value of

|\alpha-\beta|

. Number of solutions of the equation

{z^2} + {\left| z \right|^2} = 0,

where

z \in C

is If

2x = - 1 + \sqrt 3 i

, then the value of

{\left( {1 - {x^2} + x} \right)^6} - {\left( {1 - x + {x^2}} \right)^6}

is equal to