Home
Class 11
MATHS
If a,b,c are integers, not all simultane...

If a,b,c are integers, not all simultaneously equal and w is cube root of unity (`w != 1)`, then minimum value of ` |a + bw + c w^2|`

Text Solution

Verified by Experts

`Z=a+bw+cw^2`
`Z=a+bw^2+cw`
`|z^2|=Z*underlineZ=(a+bw+cw^2)(a+bw^2+cw)`
`=a^2+b^2+c^2+abw^2+acw+acw^2+bcw+bcw^2+abw`
`|Z|^2=a^2+b^2+c^2-ab-bc-ac`
`|z|^2=((a-b)^2+(b-c)^2+(a-c^2))/2`
`|z|=sqrt((a-b)^2+(b-c)^2+(a-c^2))/2`
a=b=n,c=n+1,n-1
...
Promotional Banner

Similar Questions

Explore conceptually related problems

a,b,c are integers,not all simultaneously equal,and omega is cube root of unity (omega!=1) then minimum value of |a+b omega+c omega^(2)| is 0 b.1 c.(sqrt(3))/(2) d.(1)/(2)

If a , b , c are integers not all equal and w is a cube root of unity (w ne 1) then find the minimum value of |a + b w + c w^(2)|

a ,b , c are integers, not all simultaneously equal, and omega is cube root of unity (omega!=1) , then minimum value of |a+bomega+comega^2| is 0 b. 1 c. (sqrt(3))/2 d. 1/2

a ,b , c are integers, not all simultaneously equal, and omega is cube root of unity (omega!=1) , then minimum value of |a+bomega+comega^2| is 0 b. 1 c. (sqrt(3))/2 d. 1/2

a ,b , c are integers, not all simultaneously equal, and omega is cube root of unity (omega!=1) , then minimum value of |a+bomega+comega^2| is 0 b. 1 c. (sqrt(3))/2 d. 1/2

If a,b,c are integers not all equal and omega is a cube root of unity (omega ne 1) , then the minimum value of |a+bomega+comega^(2)| is

If a, b, c are integers, no two of them being equal and omega is complex cube root of unity, then minimum value of |a+b omega| + c omega^(2)| is

If a,b,c are distinct odd integers and omega is non real cube root of unity,then minimum value of |a omega^(2)+b+c omega|, is