If $w=\cos (\pi / n)+i \sin (\pi / n)$, then value of $1+w+$ $w^2+\cdots+w^{n-1}$ is

JEE MATHEMATICS MCQ: COMPLEX NUMBERS

1 Medium

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Application +4 | -1

w=\cos (\pi / n)+i \sin (\pi / n)

, then value of

1+w+

w^2+\cdots+w^{n-1}

View answer and explanation

Correct option: C

1+i \cot (\pi / 2 n)

Option C (

1+i \cot (\pi / 2 n)

) is correct because after simplifying the geometric series and using trigonometric identities, the expression equals

1+i \cot (\pi / 2 n)

Practice All Chapter MCQs →

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|z|=1

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\left|\sum\limits_{r=1}^n z_r\right|

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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}