Negative imaginary exponents I was reading this question earlier: Understanding imaginary exponents
In the answer, the answerer says

$A^i=x+iy$
Furthermore, we can write $A^{−i}=x−iy$ for the same $x$ and $y$.

Can someone explain to me why this is true? It kind of makes sense to me but how can we make the leap to just negating the imaginary component?

Hint:
$$A^i=x+iy$$
$$A^{-i}=\frac{1}{A^{i}}=\frac{1}{x+iy}=\frac{1}{x+iy}\cdot\frac{x-iy}{x-iy}=\frac{x-iy}{x^2+y^2}=x-iy$$
Note :
it says
$$|A^i|=1$$
$$|A^i|=\sqrt{x^2+y^2}=1$$
$$\Rightarrow x^2+y^2=1$$
