z=m+ni
|2z+15|=√3|z＋10|
|2z+15|^2=3|z＋10|^2
|2z+15|^2=|(2m+15)+2ni|^2=(2m+15)^2+4n^2
|z+10|^2=|(m+10)+ni|^2=(m+10)^2+n^2
所以4m^2+60m+225+4n^2=3m^2+60m+300+3n^2
m^2+n^2=75
所以|z|=√(m^2+n^2)=5√3
z/a+a/z
=(m+ni)/a+a/(m+ni)
=(m+ni)/a+a(m-ni)/(m^2+n^2)
=[(m^2+n^2)(m+ni)+a^2(m-ni)]/a(m^2+n^2)
={[m(m^2+n^2)+a^2m]+[n(m^2+n^2)-a^2n]}/a(m^2+n^2)
是实数,虚部为0
[n(m^2+n^2)-a^2n]/a(m^2+n^2)=0
n(m^2+n^2)-a^2n=0
z是虚数,所有n不等于0
a^2=m^2+n^2
a=±5√3