MyQuestionIcon

1

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

Properties of Cube Root of a Complex Number

If ω is a c...

Question

If $ω$ is a cube root of unity, then $(1 + ω - ω^{2})^{5} + (1 - ω + ω^{2})^{5} =$

A

32

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

B

31

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

C

30

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

D

28

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

Open in App

Solution

The correct option is A 32
$1 + w = - w^{2}$
$1 + w^{2} = - w$
Hence,
$(- 2 w^{2})^{5} + (- 2 w)^{5}$
$= - 2^{5} (w + w^{2})$
$= 32$

Suggest Corrections

thumbs-up

1

Similar questions

ω

is complex cube root of unity , then

(1 - ω + ω^{2})^{6} + (1 - ω^{2} + ω)^{6} =

ω

is a complex cube root of unity then

∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 + ω & 1 + ω^{2} 1 + ω & 1 + ω^{2} & 1 1 + ω^{2} & 1 & 1 + ω \end{matrix} ∣ ∣ ∣ ∣ ∣ =

^{'} ω^{'}

is a complex cube root of unity, then

(1 - ω + w^{2})^{7} + (1 + ω - ω^{2})^{7} =

ω

is a complex cube root of unity, then the value of

(1 + ω) (1 + ω^{2}) (1 + ω^{4}) (1 + ω^{8}) . . . (2 n + 1)

1, ω, ω^{2}

are three cube roots of unity, then

(1 - ω + ω^{2}) (1 + ω - ω^{2})

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

What Is a Good Fuel?

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Properties of Cube Root of a Complex Number

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon