Home
Class 12
MATHS
If p=a+bomega+comega^2;q=b+comega+aomega...

If `p=a+bomega+comega^2;q=b+comega+aomega^2` and `r=c+aomega+bomega^2` where `a,b,c!=0` and `omega` is the complex cube root of unity, then

A

`p+q+r=a+b+c`

B

`p^2+q^2+r^2=a^2+b^2+^2c`

C

`p^2+q^2+r^2=-2(pq+qr+rp)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBER

    MOTION|Exercise EXERCISE - 1 (OBJECTIVE PROBLEMS I JEE MAIN) - SECTIONS - M, N & O|9 Videos
  • COMPLEX NUMBER

    MOTION|Exercise EXERCISE - 1 (OBJECTIVE PROBLEMS I JEE MAIN) - SECTIONS - S|2 Videos
  • COMPLEX NUMBER

    MOTION|Exercise EXERCISE - 1 (OBJECTIVE PROBLEMS I JEE MAIN) - SECTIONS -K|2 Videos
  • CIRCLE

    MOTION|Exercise Exercise - 4 | Level - II (Previous Year | JEE Advanced|22 Videos
  • CONTINUITY

    MOTION|Exercise EXERCISE - 4 (LEVEL -II) (PREVIOUS YEAR JEE ADVANCED)|5 Videos

Similar Questions

Explore conceptually related problems

If p=a+b omega+c omega^(2);q=b+c omega+a omega^(2) and r=c+a omega+b omega^(2) where a,b,c!=0 and omega is the complex cube root of unity,then

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=

(1)/(a + omega) + (1)/(b+omega) +(1)/(c + omega) + (1)/(d + omega) =(1)/(omega) where, a,b,c,d, in R and omega is a complex cube root of unity then find the value of sum (1)/(a^(2)-a+1)

The value of (a+bomega+comega^2)/(b+comega+aomega^2)+(a+bomega+comega^2)/(c+aomega+bomega^2) (where 'omega' is the imaginary cube root of unity), is a.-omega b. omega^2 c. 1 d. -1

If z is a complex number satisfying |z-3|<=4 and | omega z-1-omega^(2)|=a (where omega is complex cube root of unity then

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 (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