Question

已知实数m,n满足m/(1+i)=1-ni(其中i是虚数单位),则双曲线mx^2-ny^2=1的离心率为

Answer 1

m/(1+i)=m(1-i)/(1+i)(1-i)=(m-mi)/(1-i²)=(m-mi)/2=1-ni

m-mi=2-2ni

m=2

m=2n n=1

双曲线为2x²-y²=1

a²=1/2 b²=1

c²=a²+b²=1/2+1=3/2

e²=c²/a²=3/2×2=3

e=√3