已知i是虚数单位,若z1=a+i,z2=a-i,若z1z2为纯虚数,则实数a=()A.-1B.0C.1D.1或-l-数学

题目简介

已知i是虚数单位,若z1=a+i,z2=a-i,若z1z2为纯虚数,则实数a=()A.-1B.0C.1D.1或-l-数学

题目详情

已知i是虚数单位,若z1=a+i,z2=a-i,若
z1
z2
为纯虚数,则实数a=(  )
A.-1B.0C.1D.1或-l
题型:单选题难度:偏易来源:不详

答案

z1
z2
=class="stub"a+i
a-i
=
(a+i)2
(a-i)(a+i)
=
a2-1+2ai
a2+1
=
a2-1
a2+1
+class="stub"2a
a2+1
i
为纯虚数,∴
a2-1
a2+1
=0
class="stub"2a
a2+1
≠0
,解得a=±1.
故选D.

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