已知复数Z满足Z的绝对值=1+3i-Z,求(1+i)^2(3+4i)^2⼀2z

2024-12-26 18:41:21
推荐回答(1个)
回答1:

z=a+bi
|z|=1+3i-z
|z|=√(a^2+b^2)
√(a^2+b^2)=1+3i-a-bi
3-b=0
b=3
√(a^2+9)=1-a
a^2+9=a^2-2a+1
a=-4
z=-4+3i
(1+i)^2(3+4i)^2/z=(2i)(-7+12i)/(-4+3i)
=(-14i-24)(-4-3i)/(16+9)
=(54+128i)/25