Question

已知复数z满足│z-4│=│z-4i│,且z+(14-z)/(z-1)为实数,求z

Answer 1

设z=x+iy

│z-4│=│z-4i│==>x=y

Im(z+(14-z)/(z-1))=0 (z=x+jy=x+jx)

==> 2x(x-3)(x+2)/(2x^2-2x+1)=0

==>x=0或3或-2

==>z=0或3+i3或-2-i2