复数|Z|=√21,ARG(Z-4)=π/3,求复数Z.
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/12 06:54:24
![复数|Z|=√21,ARG(Z-4)=π/3,求复数Z.](/uploads/image/z/1910426-50-6.jpg?t=%E5%A4%8D%E6%95%B0%7CZ%7C%3D%E2%88%9A21%2CARG%28Z-4%29%3D%CF%80%2F3%2C%E6%B1%82%E5%A4%8D%E6%95%B0Z.)
x){
5Q5:f8kDhڞo7y J&Hv6^kb[_,14rEv5&EFڙE@3,Ά'Tը)[XTAx0PY#C&C3m""1 SQkQmik"[C${l-3!$ف
复数|Z|=√21,ARG(Z-4)=π/3,求复数Z.
复数|Z|=√21,ARG(Z-4)=π/3,求复数Z.
复数|Z|=√21,ARG(Z-4)=π/3,求复数Z.
z-4=r(cosπ/3+isinπ/3)
r>0
z=(4+r/2)+ir√3/2)
所以|z|²=(4+r/2)²+(r√3/2)²=21
16+4r+r²/4+3r²/4=21
(r-1)(r+5)=0
r>0
r=1
所以z=9/2+i√3/2