设z=a+bi,且a,b满足a(1+i)³+(2-5i)=bi-4,则z的共轭复数=
问题描述:
设z=a+bi,且a,b满足a(1+i)³+(2-5i)=bi-4,则z的共轭复数=
答
(1+i)²=1+2i-1=2i
所以2ai(1+i)+2-5i=bi-4
(-2a+2)+(2a-5)i=bi-4
所以-2a+2=-4
2a-5=b
a=3,b=1
所以z的共轭=a-bi=3-i