Can I have your help with an algebra/complex numbers related question?

Question

Question :

What is the least possible integer for n, such that [(1+i)(1-i)]^n = 1.

Note that i is the squre root of -1.

First I multiplied both numerator & denominated by (1+i) to get,

[(1+i)/(1-i)]^n = [ (1 + 2i - 1)/2]^n = (i)^n

==> i^n = 1

I know a real valued multiple of 4 would do, but how can we find the least possible integer valued n which suits This, How do we present it?

Answer 1

Since you know that n must be a multiple of 4,
Just pick n=4
It's clear that
i^1 = i
i^2 = -1
i^4 = (i^2)^2 = (-1)^2 = 1

Of course, i^0 is also 1, but maybe you wanted a positive integer...

Answer 2

So the question is asking for the least possible integer for n. In this case-4 , -8 etc. Would work too right?
How do we could pick the smallest one?