Roots of quadratic equations

$x^{2}+1=0$ has imaginary roots, but they are not equal. Its roots are $x=i$ , and $x=-i$ .

$x^{2}-1=0$ has real roots. so it does not fit the question. But the roots are $x=1$ , and $x=-1$ .

$x^{2}-2ix+1=0$ has imaginary roots and if you want to know its roots, visit this site. This site

$x^{2}-2ix-1=0$ has an equal root and it is imaginary. So it fits the question. And the root is $x=i$ .

$x^{2}=0$ has an equal root but it is not imaginary, it is a real root. And it is $x=0$ .