I'm currently reading some notes on Complex Numbers and came across this 'proof' regarding the equality of complex numbers.
Claim: Two complex numbers $a+bi$ and $c+di$ are equal iff $a=b$ and $c=d$, where $a,b,c,d$ are real numbers.
Now this is an obviously true statement, but I had a problem with the proof provided.
This is only possible iff $a=c$ and $b=d$ and so both the forward and converse are true.
I can see that this indeed proves the forward statement, but I had issues with the converse. I'd be okay with this if every single step works both ways, but the third line involves squaring both sides, which unless I'm mistaken does not work both ways.
Is there indeed an issue with this proof?