实数m取何值时,复数z=(m²-3m)+(2m²-5m-3)i是①实数?②虚数?③纯虚数?
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![实数m取何值时,复数z=(m²-3m)+(2m²-5m-3)i是①实数?②虚数?③纯虚数?](/uploads/image/z/601859-11-9.jpg?t=%E5%AE%9E%E6%95%B0m%E5%8F%96%E4%BD%95%E5%80%BC%E6%97%B6%2C%E5%A4%8D%E6%95%B0z%3D%EF%BC%88m%26%23178%3B-3m%EF%BC%89%2B%EF%BC%882m%26%23178%3B-5m-3%EF%BC%89i%E6%98%AF%E2%91%A0%E5%AE%9E%E6%95%B0%3F%E2%91%A1%E8%99%9A%E6%95%B0%3F%E2%91%A2%E7%BA%AF%E8%99%9A%E6%95%B0%3F)
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实数m取何值时,复数z=(m²-3m)+(2m²-5m-3)i是①实数?②虚数?③纯虚数?
实数m取何值时,复数z=(m²-3m)+(2m²-5m-3)i是①实数?②虚数?③纯虚数?
实数m取何值时,复数z=(m²-3m)+(2m²-5m-3)i是①实数?②虚数?③纯虚数?
①实数
2m²-5m-3=0
(2m+1)(m-3)=0
m=-1/2或m=3
②虚数
2m²-5m-3≠0
(2m+1)(m-3)≠0
m≠-1/2且m≠3
③纯虚数
m²-3m=0
m(m-3)=0
m=0,m=3
2m²-5m-3≠0
m≠-1/2且m≠3
∴m=0