What does $i^4$ equal?

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Answer 1 · 2017-02-01T13:36:40

$i^4=1$

By definition, $i=sqrt(-1)$ .

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

When we have a number, say $sqrt2$ and we multiply it by another $sqrt2$ , we get what's inside the square root sign:

$sqrt2xxsqrt2=2$

So let's apply that to our problem:

$sqrt(-1)^2=-1$

But our problem has four $i$ , not two. So let's break it down into two sets of two:

$sqrt(-1)^4=sqrt(-1)^(2+2)=sqrt(-1)^2xxsqrt(-1)^2=-1xx-1=1$

We could also have done it this way:

$sqrt(-1)^4=sqrt(-1)^(2xx2)=(sqrt(-1)^2)^2=(-1)^2=1$

What does i^4i^4 equal?