How do you simplify #i^9-i^-5#?

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Answer 1 · 2016-12-18T07:04:21

The answer is #=2i#

We use

#i^2=-1#

#i^3=-i#

#i^4=1#

#i^5=i#

#i^14=i^(3*4+2)=1*i^2=-1#

Therefore,

#i^9-i^(-5)=i^9-1/i^5#

#=(i^14-1)/i^5#

#=(-1-1)/i#

#=-(2i)/i^2#

#=2i#