How do you simplify $i^752$ ?

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Answer 1 · 2016-01-24T23:53:21

$1$

Recall that $i=sqrt(-1)$ . Because of this, $i^2=-1$ . We can then use this fact to find $i^4$ :

$i^2=-1$
$(i^2)^2=(-1)^2$
$i^4=1$

The fact that $i^4=1$ is very useful. In fact, $i^752$ can be expressed solely in terms of $i^4$ .

Since $188xx4=752$ , we can say that

$i^752=(i^4)^188$

And $i^4=1$ , so

$i^724=1^188=1$

How do you simplify i^752i^752?