Question

Find the value of

(i) ω¹⁸ 

(ii) ω²¹

(iii) ω^-30

(iv) ω^-105 

Answer 1

ω³ = 1

(i) ω¹⁸ = (ω³)⁶ = (1)⁶ = 1

(ii) ω²¹ = (ω³)⁷ = (1)⁶ = 1

(iii) ω^-30 = (ω³)^-10 = (1)^-10 = \(\frac{1}{(1)^{10}}\) = 1

(iv) ω^-105 = (ω³)^-35 = (1)^-35 = \(\frac1{(1)^{35}}\) = 1