標題:
What is De Movre's Theorem
發問:
What is "De Movre's Theorem" ? i saw a A.maths question in HKCEE 1997 paper ... Using De Movre's Theorem ,show that : XXXXX just tell me what is De Movre's Theorem is enough thx ! 更新: oh , sorry . It is Moivre's Theorem
最佳解答:
de Moivre's formula, named after Abraham de Moivre, states that for any complex number (and, in particular, for any real number) x and any integer n it holds that (cosx+isinx)^n = cos(nx)+ isin(nx) Proof:(By mathematical induction) Assume (cosx+isinx)^k = cos(kx)+isin(kx) is true when n=k+1 LHS= (cosx+isinx)^k+1 (cos+isinx)^k X (cos+isinx) = [cos(kx)+isin(kx)](cosx+isinx) = (cosx)[cos(kx)]+[i^2(sinx)[sin(kx)]+ i[cos(kx)sinx+sin(kx)cosx] = cos[(k+1)x]+sin[(k+1)x] = 0 for n
其他解答:
呢個Theorem 是一套用來幫你計數的工具,原本好複雜的數可因此簡單左 你去呢度check下就知http://www.netsoc.tcd.ie/~jgilbert/maths_site/applets/complex_numbers/de_moivre_s_theorem.html
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