作者JohnMash (Paul)
看板Math
标题Re: [中学] 教甄考题问
时间Thu May 26 00:19:58 2011
※ 引述《newperson (123456)》之铭言：
: z z^2
: 2、已知z为一虚数 若z1=-------与z2=------皆为实数
: complex 1+z^2 1+z
: -1±√3i
: 则z=____________(----------)
: 2
z/(1+z^2)=z'/(1+z'^2).............(1)
z^2/(1+z)=z'^2 / (1+z')...........(2)
by (1),(2)
z'+z'z^2=z+zz'^2...............(3)
z'^2 + zz'^2 = z^2 +z^2 z'......(4)
by (3),(4)
z'-z = zz'(z'-z)........(5)
(z'-z)(z'+z)=zz'(z-z').......(6)
by (5),(6)
zz'=1, z'+z=-1
hence,
z and z' are the roots of
x^2+x+1
--
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1F：推 newperson :感谢:) 05/26 10:51