Home
Class 12
MATHS
Prove that (1+w)(1+w^2)(1+w^4)(1+w^8)=1 ...

Prove that `(1+w)(1+w^2)(1+w^4)(1+w^8)=1` where w is the imagination cube root of unity.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • CO-ORDINATE GEOMETRY OF TWO DIMENSIONS (CONIC SECTION)

    MAHAVEER PUBLICATION|Exercise QUESTION BANK|110 Videos

  • CONTINUITY OF A FUNCTION

    MAHAVEER PUBLICATION|Exercise QUESTION BANK|21 Videos

Similar Questions

Explore conceptually related problems

The value of the expression (1+(1)/(w))(1+(1)/(w^(2)))+(2+(1)/(w))(2+(1)/(w^(2)))+(3+(1)/(w))(3+(1)/(w^(2)))+......+(n+(1)/(w))(n+(1)/(w^(2))) where w is an imaginary cube root of unity

Prove that |[1,w^2,w^2],[w^2,1,w],[w^2,w,1]|=-3w where w is a cube root of unity.

The value of the determinant |(1,omega^(3),omega^(5)),(omega^(3),1,omega^(4)),(omega^(5),omega^(4),1)| , where omega is an imaginary cube root of unity, is

Evaluate: | (1, 1, 1), (1, omega^2, omega), (1, omega, omega^2)| (where omega is an imaginary cube root unity).

The value of the expression (1+1/omega)(1+1/omega^(2))+(2+1/omega)(2+1/omega^(2))+(3+1/omega)(3+1/omega^(2))+…………..+(n+1/omega)(n+1/omega^(2)) , where omega is an imaginary cube root of unity, is

The area of a quadrilateral whose vertices are 1,i,omega,omega^(2), where (omega!=1) is a imaginary cube root of unity, is

What is sqrt((1+_(omega)^(2))/(1+_(omega))) equal to, where omega is the cube root of unity ?

If (1)/(a+omega)+(1)/(b+omega)+(1)/(c+omega)+(1)/(d+omega)=(1)/(omega) where a,b,c,d in R and omega is cube root of unity then show that sum(1)/(a^(2)-a+1)=1