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?

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