JEE MATHEMATICS MCQ: COMPLEX NUMBERS

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Analyzing +4 | -1

Let

\mathrm{z}=1+

ai be a complex number,

a>0

, such that

\mathrm{z}^{3}

is areal number. Then the sum

1+\mathrm{z}+\mathrm{z}^{2}+\ldots+\mathrm{z}^{11}

is equal to:

View answer and explanation

Correct option: B

-1365 \sqrt{3} \mathrm{i}

Option B (

-1365 \sqrt{3} i

) is correct because by finding the value of 'a' such that

z^3

is real and then summing the geometric series, we get

-1365 \sqrt{3} i

More Questions from COMPLEX NUMBERS

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

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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

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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}