JEE MATHEMATICS MCQ: COMPLEX NUMBERS

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Application +4 | -1

if locus of point

p(z)

which satisfies

\arg (3+z+z+|z| i)=\frac{\pi}{4}

is a part of conic

\mathrm{C}

then length of latus rectumof

\mathrm{C}

View answer and explanation

Correct option: D

Option D (6) is correct because the length of the latus rectum of the hyperbola is 6, derived from simplifying the given argument condition and converting it to the standard hyperbola form.

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