Question 22
Consider the statements:
$$
\text{(I) }\sqrt{a^2+b^2}=0
$$ $$
\text{(II) }\sqrt{a^2+b^2}=ab
$$ $$
\text{(III) }\sqrt{a^2+b^2}=a+b
$$ $$
\text{(IV) }\sqrt{a^2+b^2}=a-b
$$
where we allow $a$ and $b$ to be real or complex numbers. Those statements for which there exist solutions other than $a=0$ and $b=0,$ are:
$$
\text{(I) }\sqrt{a^2+b^2}=0
$$ $$
\text{(II) }\sqrt{a^2+b^2}=ab
$$ $$
\text{(III) }\sqrt{a^2+b^2}=a+b
$$ $$
\text{(IV) }\sqrt{a^2+b^2}=a-b
$$
where we allow $a$ and $b$ to be real or complex numbers. Those statements for which there exist solutions other than $a=0$ and $b=0,$ are: