a)Express i+1/i-1 in the form of m+ni,where m and n are real numbers. b)Using (a) or otherwise,simplify (i+1/i-1) ^2015?
回答 (1)
2017-01-15 8:28 am
a)Express (i+1)/(i-1) in the form of m+ni，where m and n are real numbers
Sol
(i+1)/(i－1)
=(i+1)^2/[(i+1)(i－1)]
=(i^2+2i+1)/(i^2－1)
=(－1+2i+1)/(－1－1)
=2i/(－2)
=－i
b)Using (a) or otherwise,simplify [(i+1)/(i-1)]^2015?
Sol
[(i+1)/(i－1)]^2015
=(－i)^2015
=(－i)^2012*(－i)^3
=1*(－1)^3*i^3
=(－1)*(－i)
=i
Sol
(i+1)/(i－1)
=(i+1)^2/[(i+1)(i－1)]
=(i^2+2i+1)/(i^2－1)
=(－1+2i+1)/(－1－1)
=2i/(－2)
=－i
b)Using (a) or otherwise,simplify [(i+1)/(i-1)]^2015?
Sol
[(i+1)/(i－1)]^2015
=(－i)^2015
=(－i)^2012*(－i)^3
=1*(－1)^3*i^3
=(－1)*(－i)
=i
收錄日期: 2021-04-30 21:59:55
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20170114163910AALGEF0