Question

If `i^(f(x)) = i^(g(x))` then can we deduce `f(x) = g(x)` ?

Answer 1

No

Explanation:

Note that `i^4 = 1`

Hence if `f(x) = g(x) + 4k` for some integer `k` then:

`i^(f(x)) = i^(g(x)+4k) = i^(g(x)) * i^(4k) = i^(g(x))`