（2014•河南模拟）复数z=a+i4+3i为纯虚数，则实数a的值为（）A．34B．-34C．43D．-43

Question

（2014•河南模拟）复数z=(a+i)/(4+3i)为纯虚数，则实数a的值为（　　）

A．(3)/(4)
B．-(3)/(4)
C．(4)/(3)
D．-(4)/(3)

Answer 1

∵复数z=(a+i)/(4+3i)=((a+i)(4−3i))/((4+3i)(4−3i))=(4a+3+(4−3a)i)/(25)=(4a+3)/(25)+(4−3a)/(25)i为纯虚数，
∴

(4a+3)/(25)＝0

(4−3a)/(25)≠0

，解得a=-(3)/(4)．
故选：B．