JEE MATHEMATICS MCQ: COMPLEX NUMBERS

1 Hard

1 of 1

Application +4 | -1

The maximum distance from the origin of coordinates to the point

z

satisfying the equation

\left| {z + \frac{1}{z}} \right| = a

View answer and explanation

Correct option: C

\frac{1}{2}\left( {\sqrt {{a^2} + 4} + a} \right)

Option C

\frac{{1}}{{2}}\left( {\sqrt {{{{a^2} + 4}}} + a} \right)

is correct because it represents the maximum distance derived by maximizing the modulus of the complex number and solving the resulting quadratic equation.

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