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Complex number

發問:

(a) Why i^2=-1? b^2=-1? c^2=-1? (b) (a+bi)(c+di)=(ac-bd)(ad+bc)i why not =ac+adi+cbi+bdi^2 =a(c+di)+bi(c+di) =(a+bi)(c+di) (c)a+bi/c+di why =ac+bd/c^2+d^2 +bc-ad/c^2=d^2 (i)

最佳解答:

a. definition, 問題同點解pi係圓周率一樣 b. ac+adi+cbi+bdi^2=ac+adi+cbi-bd=(ac-bd)+(ad+bc)i 你睇漏左個加 c. (a+bi)/(c+di) =(a+bi)(c-di)/(c+di)(c-di) =[(ac-bd)+(ad+bc)i]/(c^2+d^2)

其他解答:

(a) i^2 = [sqrt (-1)]^2 = -1 i = sqrt (-1) is the definition, but it does not necessarily imply that i^2 = -1 is also the definition.