Guest

If 1,ω,ω 2 ,…….ω n-1- are nth roots of unity, then (1-ω)(1-ω 2 )…(1-ω n-1 ) is equal to



If 1,ω,ω2,…….ωn-1- are nth roots of unity, then (1-ω)(1-ω2)…(1-ωn-1) is equal to



Grade:

1 Answers

Navjyot Kalra
askIITians Faculty 654 Points
13 years ago

Dear Mahima,

 

Since,1,w,w2,….,wn-1 are the nth roots of unity, therefore

        xn-1=(x-1)(x-w)(x-w2)…(x-wn-1)

        Þ (x-w)( x-w2)..( x-wn-1)=

Þ (x-w)( x-w2)..( x-wn-1)=1+x+x2+…+xn-1

        Putting x=1 in above equation, we have (1-w)(1-w2)….(1-wn-1)=n

 So the value is equal to " n ".

askIITians.com provides online iit jee courses and IIT JEE Test Series with IITians. Click here to get free online test series and check your status timely or you can join us as our registered user for getting best iit jee study material or iit jee test series.

Click here to find IIT JEE Packages or course details with askIITians.

for further details visit the folowing links:

http://www.askiitians.com//iit-jee-online-coaching.aspx

http://www.askiitians.com/iit-jee-test-series.aspx

http://www.askiitians.com/iit-study-material/

Askiitians provide you all the best possible information, feel free to ask.

all the best.

thanks and regards.

Akhilesh Shukla

Think You Can Provide A Better Answer ?

ASK QUESTION

Get your questions answered by the expert for free