已知复数z=(-1+3i)*(1-i)-(1+3i),w=z=ai(a属于R),当|w/z|≤根号2时,求a的取值范围._数学解答

已知复数z=(-1+3i)*(1-i)-(1+3i),w=z=ai(a属于R),当|w/z|≤根号2时,求a的取值范围.

人气：262 ℃　时间：2020-04-13 19:45:02

解答

z=(-1+3i)*(1-i)-(1+3i)=2+4i
|z|=√20=2√5
|w|=|a|
|w/z|=|Z|/|w|=2√5/|a|≤√2
|a|≥√10 且a不为0
-√10≤ a ≤√10且a不为0