导数代数{(1+2i)i^100+[(1-i)/(1+i)]^5}^2-[(1+i)/根号2]^20希望能尽量详细,好让我知道哪步错了

Question

导数代数
{(1+2i)i^100+[(1-i)/(1+i)]^5}^2-[(1+i)/根号2]^20
希望能尽量详细,好让我知道哪步错了

Answer 1

i^100=(i^4)^25=1^25=1 (1-i)/(1+i) =(1-i)^2/(1^2-i^2) =(1-2i-1)/(1+1) =-i 所以[(1-i)/(1+i)]^5 =(-i)^5 =-i^5 =-i (1+i)/√2 =√2(cosπ/4+isinπ/4)/√2 所以[(1+i)/√2]^20 =(cosπ/4+isinπ/4)^20 =cos20π/4...