CameraIcon

SearchIcon

MyQuestionIcon

2

You visited us 2 times! Enjoying our articles? Unlock Full Access!

nth Root of a Complex Number

If 1, ω, ω2, ...

Question

$I f 1, ω, ω^{2}, ω^{3} . . . . ., ω^{n - 1} a r e t h e n, n^{t h} r o o t s o f u n i t y, t h e n (1 - ω) (1 - ω^{2}) . . . . . (1 - ω^{n - 1}) e q u a l s$

A

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

B

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

C

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

D

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

Open in App

Solution

The correct option is C
$S i n c e 1, ω, ω^{2}, ω^{3}, . . . . . ω^{(} n - 1) a r e t h e n, n^{t h} r o o t s o f u n i t y, t h e r e f o r e, w e h a v e t h e i d e n t i t y = (x - 1) (x - ω) (x - ω^{2}) . . . . . (x - ω^{n - 1}) = x^{n} - 1 o r (x - ω) (x - ω^{2}) . . . . . . (x - ω^{n - 1}) = \frac{x^{n} - 1}{x - 1} = x^{n - 1} + x^{n - 2} + . . . . + x + 1 P u t t i n g x = 1 o n b o t h s i d e s, w e g e t (1 - ω) (1 - ω^{2}) . . . . . (1 - ω^{n - 1}) = n$

Suggest Corrections

thumbs-up

0

Similar questions

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})

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^{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})

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}) =

Q. The value of the expression

(1 + \frac{1}{ω}) (1 + \frac{1}{ω^{2}}) + (2 + \frac{1}{ω}) (2 + \frac{1}{ω^{2}}) + (3 + \frac{1}{ω^{2}}) (3 + \frac{1}{ω^{2}}) + . . . . . . . . . . . . . + (n + \frac{1}{ω}) (n + \frac{1}{ω^{2}})

ω

is the root of unity) is

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