Question

若复数 z 满足:z+z(共轭复数)=2,z·z(共轭复数)=2,则|z-z(共轭复数)|=______________

Answer 1

设 z=a+bi

z(共轭复数)=a-bi

z+z(共轭复数)=2a=2 →a=1

z·z(共轭复数)=a^2+b^2=1+b^2=2 →b=±1

|z-z(共轭复数)|=|-2b|=2