设i是虚数单位,若复数z满足z1+i=2?3i,则复数z的虚部为______

设i是虚数单位,若复数z满足z1+i=2?3i,则复数z的虚部为______.
2025-04-01 16:03:10
推荐回答(2个)
回答1:

∵复数z满足

z
1+i
=2?3i,∴
z(1?i)
(1+i)(1?i)
=2?3i
,化为z(1-i)(1+i)=2(2-3i)(1+i),∴z=5-i,
故复数z的虚部为-1.
故答案为-1.

回答2:

若复数z满足(2-i)×z=i
i为虚数单位,

z=i/(2-i)
=i(2+i)/(2-i)(2+i)
=(2i-1)/5
=-1/5
+2/5i
所以
则z的虚部为2/5.