How do you simplify #i^41#?

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Answer 1 · 2018-07-07T15:51:27

See explanation.

To simplify this expression first let's calculate some low powes of #i#:

From this calculations we can write that:

#i^41=i^40*i=(i^4)^10*i=1^10*i=i#

Answer 2 · 2018-07-07T15:56:45

#i#

We know that

#i^2=-1#

#i^3=-i#

#i^4=1#

This may be a less intuitive way of going about this, but let's see:

The imaginary unit follows a pattern. From #i^1# to #i^4#, it goes

#i,-1,-i,1#

Every time the exponent increases by #4#, we start the pattern over. This means that when our power of #i# is

#5, 9, 13, 17, 21, 25, 29, 33, 37, color(blue)(41)#

We will be equal to #i#. Now we see that #i^41=i#

Hope this helps!