Question

設(shè)m∈R，復(fù)數(shù)z＝2m²－3m－2＋(m²－3m＋2)i.試求m為何值時(shí)，z分別為：
(1)實(shí)數(shù)；(2)虛數(shù)；(3)純虛數(shù)

Answer 1

(1)當(dāng)z為實(shí)數(shù)時(shí)，則有m²－3m＋2＝0，解得m＝1或2.即m為1或2時(shí)，z為實(shí)數(shù)．
(2)當(dāng)z為虛數(shù)時(shí)，則有m²－3m＋2≠0，解得m≠1且m≠2.即m≠1且m≠2時(shí)，z為虛數(shù)．
(3)當(dāng)z為純虛數(shù)時(shí)，則有2m²－3m-2＝0且m²－3m＋2≠0，解得m＝，即m＝

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