若i是虚数单位,且复数(b+i)/(a-i)=1+i(a,b∈R),则a+b=
问题描述：
若i是虚数单位,且复数(b+i)/(a-i)=1+i(a,b∈R),则a+b=
答
(b+i)/(a-i)=(b+i)(a+i)/[(a-i)(a+i)]=(ab+(a+b)i-1)/(a^2+1)=(ab-1)/(a^2+1) + (a+b)i/(a^2+1)=1+i故(ab-1)/(a^2+1)=1且(a+b)/(a^2+1)=1得a^3-2a^2+a-2=0即(a^2+1)(a-2)=0故a=2,b=3故a+b=5