Let omega= e^((ipi)/3) and a, b, c, x,...

Let ` omega= e^((ipi)/3) and a, b, c, x, y, z` be non-zero complex numbers such that `a+b+c = x, a + bomega + comega^2 = y, a + bomega^2 + comega = z`.Then, the value of `(|x|^2+|y|^2|+|y|^2)/(|a|^2+|b|^2+|c|^2)`

Similar Questions

Explore conceptually related problems

If x = a + b, y = a omega + b omega^2, z = aomega^2 + b omega , show that (i) xyz = a^3 + b^3

If a ,b , c are nonzero real numbers such that |b cc a a b c a a bb c a bb cc a|=0,t h e n 1/a+1/(bomega)+1/(comega^2)=0 b. 1/a+1/(bomega^2)+1/(comega^)=0 c. 1/(aomega)+1/(bomega^2)+1/c=0 d. none of these

Let 'a' and 'b' be non-zero real numbers. Then, the equation (ax^2+ by^2+c) (x^2-5xy+6y^2) represents :

The minimum value of P=b c x+c a y+a b z , when x y z=a b c , is

If x=c y+b z ,y=a z+c x ,z=bx+a y ,w h e r ex ,y ,z are not all zeros, then find the value of a^2+b^2+c^2+2a b c dot

If omega ne 1 is a cube root of unity, then show that (a+bomega+comega^(2))/(b+comega+aomega^(2))+(a+bomega+comega^(2))/(c+aomega+bomega^(2))=1

Prove that |a x-b y-c z a y+b x c x+a z a y+b x b y-c z-a x b z+c y c x+a z b z+c y c z-a x-b y|=(x^2+y^2+z^2)(a^2+b^2+c^2)(a x+b y+c z)dot

If the planes x-c y-b z=0,c x-y+a z=0a n d b x+a y-z=0 pass through a straight line, then find the value of a^2+b^2+c^2+2a b c dot

Value of [[x+y, z,z ],[x, y+z, x],[y, y, z+x]], where x ,y ,z are nonzero real number, is equal to x y z b. 2x y z c. 3x y z d. 4x y z

Let ` omega= e^((ipi)/3) and a, b, c, x, y, z` be non-zero complex numbers such that `a+b+c = x, a + bomega + comega^2 = y, a + bomega^2 + comega = z`.Then, the value of `(|x|^2+|y|^2|+|y|^2)/(|a|^2+|b|^2+|c|^2)`

Similar Questions

Recommended Questions