JEE MATHEMATICS MCQ: COMPLEX NUMBERS

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Application +4 | -1

If the complex numbers

{z_1} = a + i,\;{z_2} = 1 + + ib,{z_3} = 0

form the vertices of equilateral triangle (

a,\;b

are real numbers between 0 and 1), then

View answer and explanation

Correct option: B

a = 2 - \sqrt 3 ,\;b = 2 - \sqrt 3

Option B (

a = 2 - \sqrt 3 ,\;b = 2 - \sqrt 3

) is correct because by using the properties of equilateral triangles and complex numbers, we can derive the values of a and b.

More Questions from COMPLEX NUMBERS

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

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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|

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\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}