复数(2i/1+i)^2=?

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/26 08:43:34
复数(2i/1+i)^2=?复数(2i/1+i)^2=?复数(2i/1+i)^2=?=(2i)²/(i+1)²=-4/(1+2i-1)=-4/2i=-2i/i²=2i(2

复数(2i/1+i)^2=?
复数(2i/1+i)^2=?

复数(2i/1+i)^2=?
= (2i)²/(i+1)²
=-4/(1+2i-1)
=-4/2i
=-2i/i²
=2i

(2i/1+i)^2=-4/(2i)=2i

(2i/1+i)^2= [ 2i*(1-i) / (1+1) ] ^2 = [ i*(1-i) ] ^2 = (1+i)^2 = 1-1+2i = 2i