↵​​ Pls answer this
If ω is imaginary cube root of unity and (a + bω + cω2)2015 = (a + bω2 + cω) where a,b,c are unequal real numbers, then a2 + b2 + c2 – ab – bc – ca is equal to- (1) 0 (2) (3) 1 (4) –1

Dear Student,
Please find below the solution to the asked query:

We havea++22015=a+2+...iTake conjugate on bot sides, we know that ω¯=ω2 and ω2¯=ω, hencea+2+2015=a++2....iii×iia++2×a+2+2015=a++2×a+2+a++2×a+2+2015a++2×a+2+=1a++2×a+2+2014=1a2+abω2+acω+abω+b2ω3+bcω2+acω2+bcω4+c2ω32014=1Use ω3=1a2+abω2+acω+abω+b2+bcω2+acω2+bcω+c22014=1a2+b2+c2+abω+ω2+bcω+ω2+caω+ω22014=1Use ω+ω2=-1a2+b2+c2-ab-bc-ca2014=1a2+b2+c2-ab-bc-ca=1 or -1 Answer

Hope this information will clear your doubts about this topic.

If you have any doubts just ask here on the ask and answer forum and our experts will try to help you out as soon as possible.

  • 1
What are you looking for?