JEE MATHEMATICS MCQ: COMPLEX NUMBERS

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Application +4 | -1

z_1, z_2, z_3

are three complex numbers, then

\left|z_2+z_3\right|^2+\left|z_3+z_1\right|^2+\left|z_1+z_2\right|^2

equal

View answer and explanation

Correct option: D

none of these

Option D (none of these) is correct because the given expression does not simplify to any of the provided options. The correct expansion involves terms with individual complex numbers and their conjugates.

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