(1)i/1+i(2)2/(1+i)^2(3)(3-i)/(3+4i)(4)(3-4i)(1+2i)/2i

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(1)i/1+i(2)2/(1+i)^2(3)(3-i)/(3+4i)(4)(3-4i)(1+2i)/2i(1)i/1+i(2)2/(1+i)^2(3)(3-i)/(3+4i)(4)(3-4i)(1+

(1)i/1+i(2)2/(1+i)^2(3)(3-i)/(3+4i)(4)(3-4i)(1+2i)/2i
(1)i/1+i
(2)2/(1+i)^2
(3)(3-i)/(3+4i)
(4)(3-4i)(1+2i)/2i

(1)i/1+i(2)2/(1+i)^2(3)(3-i)/(3+4i)(4)(3-4i)(1+2i)/2i
【1】
i/(1+i)=[i(1-i)]/[(1+i)(1-i)]=[i-i²]/[1-i²]=(i+1)/(2)=(1/2)+(1/2)i
【2】
2/(1+i)²=2/(1+2i+i²)=2/(2i)=1/i=-i
【3】
(3-i)/(3+4i)=[(3-i)(3-4i)]/[(3+4i)(3-4i)]=(5-15i)/(25)=(1/5)-(3/5)i
【4】
(3-4i)(1+2i)/(2i)=(11+2i)/(2i)=(11/2i)+1=1-(11/2)i

i/1+i=i(1-i)/(1-i²)=(i-i²)/2=(1+i)/2
类似的其他题目都是如此
(a+bi)/(c+di)
=(a+bi)(c-di)/[(c+di)(c-di)]
=(a+bi)(c-di)/(c²+d²)

1、i/(1+i)=i(1-i)/2=0.5i+0.5

2、2/(1+i)²=2/(2i)=1/i=-i

3、(3-i)/(3+4i)=(3-4i)(3-i)/25=(5-15i)/25=(1-3i)/5

4、(3-4i)(1+2i)/(2i)=(3+8+2i)/(2i)=-(11+2i)i//2=-5.5i+1