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$i^{3600}=(i^4)^{900}=1$ $i^4=\sqrt[900]{1}=\boxed{1}$

Assuming $i = \sqrt {-1}$ the answer is $1$

But if you didn't know that then

$i^{3600} = (i^4)^{900}$

Since we know $i^{3600} = 1$ we can substitute

$1 = (i^4)^{900}$

When putting $1$ to the $n^{th}$ power the answer will always be $1$ . In other words

$1^n = 1$

Since we need to find the $900$ th root of $1$ we can just put it into the formula as $n = \frac {1}{900}$ . This means that

$1^{\frac {1}{900}} = i^4 \Rightarrow 1 = i^4$

All in all the answer is $1$ no matter which way you look at it

since,i^2=-1 ,so i^4=1