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,

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

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

$=(-1-1)/i$

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

$=2i$

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