推 newperson :感謝:) 05/26 10:51
※ 引述《newperson (123456)》之銘言：
: z z^2
: 2、已知z為一虛數 若z1=-------與z2=------皆為實數
: complex 1+z^2 1+z
: -1±√3i
: 則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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