MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

nth Root of a Complex Number

If ω is an nt...

Question

If $ω$ is an n^th root of unity, other than unity, then the value of $1 + ω + ω^{2} + . . . . + ω^{n - 1}$ is
[Karnataka CET 1999]

A

\N

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

B

1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

C

-1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

D

None of these

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A \N
$1 + ω + ω^{2} + . . . . + ω^{n - 1} = (\frac{ω^{n} - 1}{ω - 1}) = 0, (∵ ω^{n} = 1)$

Suggest Corrections

thumbs-up

0

Similar questions

1, ω, ω^{2}, . . ., ω^{n - 1}

n^{t h}

roots of unity, then the value of

(5 - ω) (5 - ω^{2}) . . . (5 - ω^{n - 1}) =

1, ω, ω^{2}

are the cube roots of unity, then their product is
[Karnataka CET 1999, 2001]

1, ω, ω^{2}, . . . . ω^{n - 1}

n, n^{t h}

roots of unity, then the value of

(9 - ω) \cdot (9 - ω^{2}) \cdot (9 - ω^{3}) . . . (9 - ω^{n - 1})

ω, ω^{2}, ω^{3}, . . . . . . . . ω^{n - 1}

are nth roots of unity then

(1 - ω) (1 - ω^{2}) . . . . . . . (1 - ω^{n - 1})

1, ω, ω^{2}, ω^{3} . . . . ., ω^{n - 1}

n^{t h}

roots of unity, then

(1 - ω) (1 - ω^{2}) . . . . . (1 - ω^{n - 1})

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

De Moivre's Theorem

MATHEMATICS

Watch in App

explore_more_icon

Explore more

nth Root of a Complex Number

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon