How do you simplify #i^59#?

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Answer 1 · 2018-06-30T20:07:38

#i^59=-i#

#i^59=i^56i^3=(i^16)^4i^3=1i^3=i^2i=-i#

Answer 2 · 2018-06-30T20:14:27

#-i#

Recall that

#i^2=-1#

#i^3=-i#

#i^4=1# (Any multiple of #4# exponent will also be #1#)

With this in mind, we can rewrite #i^59#, since the exponent is a prime number.

#i^59=color(blue)(i^56)*i^3#

Since #56# is a multiple of #4#, #i^56=1#. What we have simplifies to:

#1*i^3=-i#

Hope this helps!

Answer 3 · 2018-06-30T20:36:36

#i^59=i^59xxi^2/i^2={(i^60)(i)}/(-1)=(i^4)^15*i/-1=1^15*-i=-i#.