问题
选择题
已知复数Z=t+i(t∈R+),且Z满足Z3∈R,则实数t的值为( )
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答案
复数Z=t+i(t∈R+),
∴Z3=(t+i)(t+i)t+i)=t3-3t+(3t2-1)i
∵Z满足Z3∈R,
∴3t2-1=0,
∴t=±
,3 3
∵t∈R+
∴t=3 3
故选B.
已知复数Z=t+i(t∈R+),且Z满足Z3∈R,则实数t的值为( )
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复数Z=t+i(t∈R+),
∴Z3=(t+i)(t+i)t+i)=t3-3t+(3t2-1)i
∵Z满足Z3∈R,
∴3t2-1=0,
∴t=±
,3 3
∵t∈R+
∴t=3 3
故选B.
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