已知复数z=m+(3m-1)i/2-i(m∈R)的实部与虚部互为相反数,求|z|
问题描述：
已知复数z=m+(3m-1)i/2-i(m∈R)的实部与虚部互为相反数,求|z|
答
z=m+(3m-1)i/2-i=m+(3m-1)i(2+i)/5=m+((3m-1)/5)(-1+2i)=((2m+1)/5)+((6m-2)/5)i所以: ((2m+1)/5=-(6m-2)/52m+1=-6m+2m=1/8z=((2m+1)/5)+((6m-2)/5)i=(1/4)-(1/4)i|z|=((1/4)^2+(1/4)^2)^(1/2)=(1/4)(根号2)