已知z1 z2是两个虚数,z1+z2与z1z2均为实数,求证z1 z2是共轭复数
RT
人气：200 ℃ 时间：2019-08-21 05:52:28
解答
z1=a+bi,z2=c+di
a,b,c,d是实数
z1+z2=a+c+(b+d)i是实数
所以b+d=0
d=-b
z1=a+bi
z2=c-bi
z1z2=(ac+b²)+(bc-ab)i是实数
所以bc-ab=0
z1=a+bi是虚数
所以b≠0
所以c-a=0
c=a
所以z1=a+bi,z2=a-bi
所以z1,z2是共轭虚数
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