Solution
= Solution
A quotient with nonzero denominator has zero <complex modulus> exactly when its numerator is zero. Thus
$$
\boxed{z=i,\quad\text{a single point}.}
$$
At that point $z^*-i=-2i\ne0$, so the solution is admissible.
= Solution
A quotient with nonzero denominator has zero <complex modulus> exactly when its numerator is zero. Thus
$$
\boxed{z=i,\quad\text{a single point}.}
$$
At that point $z^*-i=-2i\ne0$, so the solution is admissible.