Research Space for Linear Algebra & Discrete Mathematics
2009-03-31
請問一下關於"Primitive root"
請問一下 什麼是"primitive root" 而"Consider the primitive 6th root w of 1" (a)Fint it's real and imaginary part (b)Which power of w is equal to 1/w (c)What is 1+w+w^2+w^3+w^4+w^5 要如何解?謝謝指教
2 則留言:
當w^6 = 1且w^1, ..., w^5皆不為1時, 稱w為primitive 6th root of unity
(a) w = exp((+-)2(pi)i/6)為二個primitive 6th root of unity
w = exp((pi)i/3)
= cos((pi)/3) + i sin((pi)/3)
(b) 1/w = w^(-1) = w^(-1)w^6 = w^5
(c) 1 + w + ... + w^5
= (w^6 - 1)/(w - 1)
= (1 - 1)/(w - 1) = 0
大概了解了 謝謝老師
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