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ǰλãҳ>>Ϊʲô e^(ix) = cosx + isinx>>

Ϊʲô e^(ix) = cosx + isinx

e^ix=cosx+isinx?e^ix = lim(ninf) (1 + ix/n)^n.ôŷʽ˵,(ұ)һתxǶ

Ϊʲô e^(ix) = cosx + isinxe^-ix=cosx-isinx,ȻʽӼķõsinx=(e^ix-e^-ix)/(2i),cosx=(e^ix+e^-ix)/2.tanx=[e^(ix)-

λ֤һŷʽe^(ix)=cosx+isinx֤õeע⣺ŷʽe^(ix)=cosx+isinxǺָͨһֹʽļԼڽƼϵ

e^(ix) = cosx + isinxŷʽ֣Ϊڶŷ(ѧ)

eô Ϊʲôܶ࿴ȥɵĹʽشeر,Ĺʽ:e^(ix)=cosx+isinx,ieͺںϵ

ŷʽ e^(ix)=cosx+isinx ܲóȵķƵ󵼵ԭiٶȵٶȳiijϵʾӵ˶ųֱ

Ϊʲô e^(ix) = cosx + isinxҪ֤,Ҫһ֪ʶ1)̩ռ2)ϣѾ߱.ȸ̩չʽ.

ŷʽe^ix=cosx+isinxôƳ?ֻ֪y=e^xy=sinxy=cosxݼչ, e^x=exp(x)=1+x/1!+x^2/2!+x^

e^xd(cosx)=e^xsindxΪʲô(0,)(e^cosx-e^(-cosx))dx xd(cosx) Ϊʲô e^(ix) = cosx + isinx ŷʽe^ix=

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