(1/a)的共轭虚数=1/(a的共轭虚数)?问:命题是否正确.求说理或证明.若不对请举反例.
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![(1/a)的共轭虚数=1/(a的共轭虚数)?问:命题是否正确.求说理或证明.若不对请举反例.](/uploads/image/z/1078913-65-3.jpg?t=%281%2Fa%29%E7%9A%84%E5%85%B1%E8%BD%AD%E8%99%9A%E6%95%B0%3D1%2F%EF%BC%88a%E7%9A%84%E5%85%B1%E8%BD%AD%E8%99%9A%E6%95%B0%EF%BC%89%3F%E9%97%AE%EF%BC%9A%E5%91%BD%E9%A2%98%E6%98%AF%E5%90%A6%E6%AD%A3%E7%A1%AE.%E6%B1%82%E8%AF%B4%E7%90%86%E6%88%96%E8%AF%81%E6%98%8E.%E8%8B%A5%E4%B8%8D%E5%AF%B9%E8%AF%B7%E4%B8%BE%E5%8F%8D%E4%BE%8B.)
(1/a)的共轭虚数=1/(a的共轭虚数)?问:命题是否正确.求说理或证明.若不对请举反例.
(1/a)的共轭虚数=1/(a的共轭虚数)?问:命题是否正确.求说理或证明.若不对请举反例.
(1/a)的共轭虚数=1/(a的共轭虚数)?问:命题是否正确.求说理或证明.若不对请举反例.
成立.
证:设a=x+yi 则a的共轭虚数=x-yi
1/a = (x-yi)/(x²+y²) 则(1/a)的共轭虚数=(x+yi)/(x²+y²)
1/(a的共轭虚数) =1/x-yi =(x+yi)/(x²+y²)
所以(1/a)的共轭虚数=1/(a的共轭虚数)
得证
命题是对的
设虚数a=x+yi,则其共轭虚数a‘ =x-yi
故1/a=1/(x+yi)=(x-yi)/(x^2 + y^2),则其共轭虚数为(x+yi)/(x^2 + y^2),
而1/(a的共轭虚数)=1/a’ =1/(x-yi),
显然x^2 + y^2=(x-yi)×(x+yi)
故(x+yi)/(x^2 + y^2)=1/(x-yi)
即(...
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命题是对的
设虚数a=x+yi,则其共轭虚数a‘ =x-yi
故1/a=1/(x+yi)=(x-yi)/(x^2 + y^2),则其共轭虚数为(x+yi)/(x^2 + y^2),
而1/(a的共轭虚数)=1/a’ =1/(x-yi),
显然x^2 + y^2=(x-yi)×(x+yi)
故(x+yi)/(x^2 + y^2)=1/(x-yi)
即(1/a)的共轭虚数=1/(a的共轭虚数),问题得证
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