设a,b∈R且b≠0,若复数(a+bi)3是实数,则( )
A. b2=3a2
B. a2=3b2
C. b2=9a2
D. a2=9b2
人气:240 ℃ 时间:2020-01-29 12:04:28
解答
(a+bi)3=a3+3a2bi-3ab2-b3i=(a3-3ab2)+(3a2b-b3)i,因是实数且b≠0,所以3a2b-b3=0⇒b2=3a2
故选A.
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