数学复数的运算(2+i)^3(4-2i)/5i(1+i)=1-7i 怎么算的求详细过程_数学解答

数学复数的运算
(2+i)^3(4-2i)/5i(1+i)=1-7i 怎么算的求详细过程

人气：457 ℃　时间：2020-03-25 08:30:08

解答

(2+i)³(4-2i)/5i(1+i)
=(8+3×4×i+3×2×i²+i³)(4-2i)/5(i-1)
=(8+12i-6-i)(4-2i)/5(i-1)
=2(2+11i)(2-i)(i+1)/5(i-1)(i+1)
=2(2+11i)(i+3)/5(-1-1)
=-(2+11i)(i+3)/5
=-(35i-5)/5
=1-7i