## Proof that if \$m^2+n^2=0\$ then \$m=0\$ and \$n=0\$

Prove that if $$m^2+n^2=0$$ then $$m=0$$ and $$n=0$$.

And this is how I do it: $$m^2+n^2=0$$ so $$m^2= -n^2$$ Because $$m,n$$ are real numbers, then $$m^2>=0$$, $$n^2>=0$$. Therefore, $$m=0$$ and $$n=0$$.

Is that correct?