已知复数z=(-1+3i)*(1-i)/i-(1+3i)/i,w=z+ai(a属于R),当|w/z|≤根号2时,求a的取值范围
问题描述：
已知复数z=(-1+3i)*(1-i)/i-(1+3i)/i,w=z+ai(a属于R),当|w/z|≤根号2时,求a的取值范围
答
z=(i^2+3i)*(1-i)/i-(3i-i^2)/i
=(i+3)*(1-i)-(3-i)
=1-i
==>w=z+ai=1+(a-1)i
==>|w|^2=a^2-2a+2,|z|^2=2
|w/z|^2≤1/2
==>a^2-2a+2≤1
==>(a-1)^2≤0
==>a=1