已知复数z1=m+2i，z2=3-4i，若z1z2为实数，则实数m的值为．

Question

已知复数z ₁ =m+2i，z ₂ =3-4i，若 (z1)/(z2) 为实数，则实数m的值为______．

Answer 1

由z ₁ =m+2i，z ₂ =3-4i，
则 (z1)/(z2) = (m+2i)/(3-4i) = ((m+2i)(3+4i))/(25) = (3m-8)/(25) + (4m+6)/(25) i 为实数，
得4m+6=0，则实数m的值为- (3)/(2) ．
故答案为： -(3)/(2)