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你可能喜欢复变函数里的主值到底什么意思?(1) ,求Ln(-i)及其主值 ,2kpi - pi/2 ) ,主值为 i3pi/2(2) ,求Ln(-3+4i)及其主值 ,ln5 - iarctan(4/3) + i(2kpi + pi)主值为 ln5 + i(pi - arctan(4/3))我看出(1)题的主值是令k=1求得的 ,而(2_作业帮
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复变函数里的主值到底什么意思?(1) ,求Ln(-i)及其主值 ,2kpi - pi/2 ) ,主值为 i3pi/2(2) ,求Ln(-3+4i)及其主值 ,ln5 - iarctan(4/3) + i(2kpi + pi)主值为 ln5 + i(pi - arctan(4/3))我看出(1)题的主值是令k=1求得的 ,而(2
复变函数里的主值到底什么意思?(1) ,求Ln(-i)及其主值 ,2kpi - pi/2 ) ,主值为 i3pi/2(2) ,求Ln(-3+4i)及其主值 ,ln5 - iarctan(4/3) + i(2kpi + pi)主值为 ln5 + i(pi - arctan(4/3))我看出(1)题的主值是令k=1求得的 ,而(2)题的主值是令k=0求得的 ,这怎么回事 没有个规定的?(2)题的答案照公式来应该是 ln5 - i( arctan(-4/3) + 2kpi ) 又arctan(-4/3)=-arctan(4/3) ,所以也可以写成 ln5 - i( -arctan(4/3) + 2kpi) 这样怎么不对?为什么答案要多加一个pi?
复数z的辐角有无穷多个,其中有一个角称为辐角的主值,如果一个复变函数的函数值与辐角有关,且是多值函数,那么辐角取主值时的一个分支就称为函数的主值了.比如对数函数Lnz=Ln(re^i(ψ+2kπ))=lnr+i(ψ+2kπ),k是任意整数,ψ是z的辐角的主值.k=0时的一个分支lnr+iψ称为Lnz的主值,记为lnz,即lnz=lnr+iψ.注意：有些书上把辐角的主值定义为[0,2π)内的角度,有的是把辐角的主值定义为-π与π之间的角.这里的答案很明显选择的是前者.
兄弟你哪个学校的啊 ？？？？你说的题和我们作业一样？？你们也用绿皮的西安交大版的教材？？？？2012行政人力资源中心KPI_百度文库
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你可能喜欢e的(2k兀i)次方为什么等于一?_作业帮
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e的(2k兀i)次方为什么等于一?
e的(2k兀i)次方为什么等于一?
e^(iθ)=cosθ+isinθ把θ=2π代入即可 证明可以用泰勒级数由e^x = 1+x+x^2/2!+x^3/3!+...+x^n/n!+..以及sin x = x-x^3/3!+x^5/5!-...(-1)^(k-1)*x^(2k-1)/(2k-1)!+... cos x = 1-x^2/2!+x^4/4!-...(-1)^k*x^(2k)/(2k)!+...
这个利用欧拉公式，e^(ix)=cos(x)+isin(x);x=2带入cos(2kpi)=cos(0)=1;
sin(2kpi)=sin(0)=0;
因为e的兀i次方+1=0且2K为偶数-1的偶数次方为1