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!

How do you simplify i^41i^41?