For how many real values of $k$ do we have $|3-ki| = 0$?
To find the real values of $k$ that make $|3-ki| = 0$, I need to use the definition of the modulus (or absolute value) of a complex number. If $z = a + bi$ is a complex number, then $|z| = \sqrt{a^2 + b^2}$, which is the distance from $z$ to the origin in the complex plane. So, $|3-ki| = \sqrt{3^2 + k^2} = 0$. This means that $3^2 + k^2 = 0$, or $k^2 = -9$. But this is impossible for any real value of $k$, since the square of a real number is always nonnegative. Therefore, there are no real values of $k$ that make $|3-ki| = 0$. 