JEE MATHEMATICS MCQ: COMPLEX NUMBERS

1 Hard

1 of 1

Application +4 | -1

\left| {{a_i}} \right| < 1,{\lambda _i} \ge 0

for

i = 1,2, \ldots .,n

and

{\lambda _1} + {\lambda _2} + \ldots + {\lambda _n} = 1,

then the value of

\left| {{\lambda _1}{a_1} + {\lambda _2}{a_2} + \ldots + {\lambda _n}{a_n}} \right|

View answer and explanation

Correct option: B

Less than 1

Option B (Less than 1) is correct because the magnitude of the weighted sum is less than 1, given the constraints on the magnitudes of a_i and the non-negative weights lambda_i.

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