已知z1=2-i,z2=a+i,且z1=1/z2,求复数a?

Question

已知z1=2-i,z2=a+i,且z1=1/z2,求复数a?

Answer 1

即z1z2=1
(2-i)(a+i)=1
2a+2i-ai+1=1
(i-2)a=2i
a=2i/(i-2)
=2i(i+2)/(-1-4)
=(2-4i)/5