[supernewton]

It is not. a and b are not symmetric in this equation, you can't just swap them.

[henry2023]

You can swap them without loss of generality (WLOG).

[davrosthedalek]

No, this is not correct. WLOG means: I assume one of the possible cases, but the proof works the same way for other cases. But that's not true here. The proof, as shown, only works for a>b>0, it does not work (without extra work or explanation) for a<b. The proof for a<b is similar, but not the same. [And it certainly does not show it for a,b element of C]

[olddustytrail]

Of course you can. What do you mean?

[Scarblac]

The answer is going to be negative regardless of the names, so this geometric proof won't work.

[davrosthedalek]

3^2-2^2 =!= 2^2-3^2.

(You can exchange a and b in, say a^2+b^2, because 2^2+3^2=3^2+2^2)