已知复数z满足z*z共轭=4,且|z+1+根号3i|=4
问题描述:
已知复数z满足z*z共轭=4,且|z+1+根号3i|=4
求z
2.求z,使它同时满足:(1)|z-4|=|z-4i|
(2)z+(14-z)分之(z-1)是实数.
答
(1) 设z=a+b*i ,则z共轭=a-b*i由已知:z*z共轭=(a+b*i)(a-b*i)=a^2+b^2=4 (1)|a+b*i+1+根号3i|=|(a+1)+(根号3+b)*i|=4 即(a+1)^2+(根号3+b)^2=16 (2) 联立(1)(2)得:a=1,b=根号3所以z=1+根号3i(2)由已...