JEE MATHEMATICS MCQ: COMPLEX NUMBERS

1 Easy

1 of 1

Application +4 | -1

{z_1}

and

{z_2}

are two complex numbers such that

\left| {\frac{{{z_1} - {z_2}}}{{{z_1} + {z_2}}}} \right| = 1,

then

View answer and explanation

Correct option: B

{z_1} = i\;k\;{z_2},\;k \in R

Option B (

{z_1} = i\\;k\\;{z_2},\\;k \in R

) is correct because the given condition implies that the diagonals of a parallelogram formed by

z_1

and

z_2

are equal, which means it's a rectangle, and thus

z_1

and

z_2

are orthogonal.

More Questions from COMPLEX NUMBERS

Practice All Chapter MCQs →

{\left| {1 - i} \right|^x} = {2^x}

|z|=1

z \neq \pm 1

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|

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

a \neq 0

\alpha, \beta

\gamma

|\alpha-\beta|

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

z \in C

2x = - 1 + \sqrt 3 i

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