题目内容：

几道微积分必学基础题
请写出 标准式 （standard form 不知道中文是不是这个）
6/i
2/4-5i
(2+i)/(2-i)
i/(4-5i)^2
perform the operation and write the result in standard form
2/(1+i)-3/(1-i)
请写出步骤! 因为我需要步骤去自习!
我给100分! 十万火急! 谢谢!

优质解答

6/i
=6i/(i)^2
=-6i
(i)^2=-1
2/(4-5i)
=2(4+5i)/[(4-5i)(4+5i)]
=(8-10i)/(16+25)
=(8-10i)/41
(2+i)/(2-i)
=(2+i)^2/[(2+i)(2-i)]
=(4+2i-1)/5
=(3+2i)/5
i/(4-5i)^2
=i/(16-40i-25)
=i/(-40i-9)
=-i/(9+40i)
=-i(9-40i)/[(9+40i)(9-40i)]
=(-40-9i)/(81+40)
=-(40+9i)/121
2/(1+i)-3/(1-i)
=2(1-i)/2-3(1+i)/2
=[2-2i-3-3i]/2
=(-1-5i)/2
一般:
k/(a+bi)
=k(a-bi)/[(a+bi)(a-bi)]
=k(a-bi)/(a^2+b^2)