If 1, \omega, \omega^2 are the cube roots of unity, k is positive integer and (1-\omega+\omega^2) ^{3 {\k}}+ (1-()^2+\omega) ^{3 {\k}}=(1-\omega+\omega)^2) ^{3 {\kk}+1}+ (1+\omega-\omega^2) ^{3 {\k}+1}, then {\k}=

AP EAPCET 17th May 2023 Shift 1 Solved Paper

Section: Mathematics

Question : 8 of 160

Marks: +1, -0

If 1,ω,ω2 are the cube roots of unity, k is positive integer and

(1−ω+ω2)3k+(1−()2+ω)3k=(1−ω+ω)2)3‌kk+1+(1+ω−ω2)3k+1,

then k=

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