JEE MATHEMATICS MCQ: COMPLEX NUMBERS

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Application +4 | -1

If the points represented by complex numbers

z_1=a+i b, z_2=c+i d

and

z_1-z_2

are collinear, where

i=\sqrt{-1}

, then

View answer and explanation

Correct option: B

a d-b c=0

Option B (

a d-b c=0

) is correct because if three complex numbers are collinear, the imaginary part of the ratio of the differences between them is zero, which leads to the given condition.

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