How do you simplify $i^37$ ?

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Answer 1 · 2018-04-27T22:28:29

$i$

First, recall that

$i=sqrt(-1)$

$i^2=-1$

$i^3=-1*sqrt(-1)=-i$

$i^4=-1*-1=1$

Whenever the exponent on $i$ is a multiple of $4$ , it will evaluate to $1$ , as imaginary numbers follow a pattern.

$36$ is a multiple of $4$ , so we know $i^36=1$ . We can rewrite $i^37$ as

$i^36*i$

$=1*i=color(blue)(i)$

Thus, $i^37=i$

Hope this helps!

How do you simplify i^37 i^37?