JEE MATHEMATICS MCQ: COMPLEX NUMBERS

1 Hard

1 of 1

Application +4 | -1

A\left( {{z_1}} \right),\;B\left( {{z_2}} \right)

and

C\left( {{z_3}} \right)

be the vertices of a triangle

ABC

in which

\angle ABC = \frac{\pi }{4}

and

\frac{{AB}}{{BC}} = \;\sqrt 2

, then the value of

{z_2}

is equal to

View answer and explanation

Correct option: C

{z_3} + i\left( {{z_1} - {z_3}} \right)

Option C (

{z_3} + i\left( {{z_1} - {z_3}} \right)

) is correct because considering the rotation about 'B' and using the given conditions leads to this result.

More Questions from COMPLEX NUMBERS

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

|z|=1

z \neq \pm 1

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\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}