JEE MATHEMATICS MCQ: COMPLEX NUMBERS

1 Medium

1 of 1

Application +4 | -1

a_1, a_2, \ldots, a_n

are real numbers and

\cos \alpha+i \sin \alpha

is a root of

x^n+a_1 x^{n-1}+a_2 x^{n-2}+\ldots+a_{n-1} x+a_n=0

(1)

then value of

\left|a_1 \cos \alpha+a_2 \cos 2 \alpha+\ldots+a_n \cos (n \alpha)\right|

View answer and explanation

Correct option: A

Option A (1) is correct because substituting the root into the polynomial and equating the real part to zero leads to the given expression being equal to -1, and taking the absolute value gives 1.

More Questions from COMPLEX NUMBERS

Practice All Chapter MCQs →

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