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JEE MATHEMATICS MCQ: COMPLEX NUMBERS

1 Easy

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Application +4 | -1

For

x_1, x_2, y_1, y_2, \in R

, if

0 < x_1, < x_2, y_1=y_2

and

z_1=x_1+i y_1, z_2=x_2+i y_2

and

z_3=\frac{1}{2}\left(z_1+z_2\right)

then

z_1, z_2, z_3

satisfy

View answer and explanation

Correct option: D

\left|z_1\right| < \left|z_3\right| < \left|z_2\right|

Option D (

\left|z_1\right| < \left|z_3\right| < \left|z_2\right|

) is correct because

z_3

is the midpoint of

z_1

and

z_2

, and

x_1 < x_2

which implies

|z_1| < |z_3| < |z_2|

.

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}

|z|=1

z \neq \pm 1

, then for any complex number

z, \frac{z}{1-z^2}

\left|z_r-r\right| \leq r, \forall r=1,2,3, \ldots, n

\left|\sum\limits_{r=1}^n z_r\right|

is less than The roots of the cubic equation

(z+a b)^3=a^3

a \neq 0

represents the vertices of a triangle. If

\alpha, \beta

\gamma

are the roots, then find the value of

|\alpha-\beta|

. Number of solutions of the equation

{z^2} + {\left| z \right|^2} = 0,

z \in C

2x = - 1 + \sqrt 3 i

, then the value of

{\left( {1 - {x^2} + x} \right)^6} - {\left( {1 - x + {x^2}} \right)^6}