In Mathematica, how can I simplify expressions like `a == b || a == -b` into `a^2 = b^2`? Every function that I have tried (including Reduce, Simplify, and FullSimplify) does not do it.

Note that I want this to work for an arbitrary (polynomial) expressions `a` and `b`. As another example,

```
a == b || a == -b || a == i b || a == -i b

```

(for imaginary `i`) and

```
a^2 == b^2 || a^2 == -b^2

```

should both be simplified to `a^4 == b^4`.

**Note:** the solution should work at the logical level so as not to harm other unrelated logical cases. For example,

```
a == b || a == -b || c == d

```

should become

```
a^2 == b^2 || c == d.

```