### Instruction: Suppose that $wz = 12-8i$, and $|w| = \sqrt{13}$.  What is $|z|$?### Response: To find $|z|$, I need to divide $|wz|$ by $|w|$, since the magnitude of a product is the product of the magnitudes.
I can find $|wz|$ by using the formula $|a+bi| = \sqrt{a^2 + b^2}$, where $a$ and $b$ are the real and imaginary parts of the complex number $a+bi$.
In this case, $a = 12$ and $b = -8$, so $|wz| = \sqrt{12^2 + (-8)^2} = \sqrt{144 + 64} = \sqrt{208}$.
Now I can divide $\sqrt{208}$ by $\sqrt{13}$ to get $|z|$.
But I want to rationalize the denominator, so I multiply both the numerator and the denominator by $\sqrt{13}$.