Home
Class 11
MATHS
If x = a + b, y= aw + bw^2 and z = aw^2 ...

If `x = a + b, y= aw + bw^2 `and `z = aw^2 + bw`, where `w` is an imaginary cube. root of unity, prove that `x^2 + y^2 + z^2 = 6ab.`

Promotional Banner

Similar Questions

Explore conceptually related problems

If x=a+b, y=aomega+bomega^2 and z=aomega^2+bomega where omega is an imaginary cube root of unity, prove that x^2+y^2+z^2=6ab .

If x=a+b, y=aomega+bomega^2 and z=aomega^2+bomega where omega is an imaginary cube root of unity, prove that x^2+y^2+z^2=6ab .

If w be an imaginary cube root of unity, prove that (1-w+w^2)^2+(1+w-w^2)^2=-4

If omega be an imaginary cube root of unity, prove that omega^4+omega^8+1/omega+1/omega^2=-2

If omega be an imaginary cube root of unity, prove that (1-omega+omega^2)(1+omega-omega^2)=4

(1+w)^7=A+Bw where w is the imaginary cube root of of a unity and A, B in R , find the ordered pair (A, B).

If omega be an imaginary cube root of unity, show that (xomega^(2)+yomega+z)/(xomega+y+zomega^(2))=omega

If x=p+q,y=p omega+q omega^(2), and z=p omega^(2)+q omega where omega is a complex cube root of unity then xyz=