z属于C,1-Z的绝对值+z＝10-3i,若Z平方＋mz＋n＋＝1-3i.1,求Z

设z=x+yi
I1-zI=√[(1-x)^2+y^2]
则√[(1-x)^2+y^2]+x+yi=10-3i
所以y=-3 √(1-2x+x^2+y^2)+x=10
1-2x+x^2+9=(10-x)^2
x^2-2x+10=100-20x+x^2
18x=90
x=5
(1) 所以z=5-3i
(2) Z平方＋mz＋n＝1-3i
(5-3i)^2+m(5-3i)+n=1-3i
25-30i-9+5m-3mi+n=1-3i
(17+5m+n)-(30+3m)i=1-3i
则30+3m=3 m=-9
17+5m+n=1
n=1+28=29