Question

若復(fù)數(shù)z＝(m²-1)+(m+1)i為純虛數(shù)，則實(shí)數(shù)m的值等于________

Answer 1

m＝1
解：復(fù)數(shù)z=(m²-1)+(m+1)i
[1]
Z是實(shí)數(shù)時(shí),必有:
m+1=0
∴m=-1
[[2]]
當(dāng)z是虛數(shù)時(shí),必有:
m+1≠0
∴此時(shí),m≠-1
[[3]]
當(dāng)z是純虛數(shù)時(shí),必有:
m²-1=0且m+1≠0
∴此時(shí),有m=1