QuestionGiven $z=9-2 i$, find $(i z-3)^{2}$ in the form $a+b i$ and show $\frac{z}{z-8}=\frac{13}{5}+\frac{16}{5} i$. Then find $\left|\frac{z}{z-8}\right|$.

Studdy Solution
Calculate the absolute value.
$$\left|\frac{z}{z-8}\right| = \sqrt{\frac{169}{25} + \frac{256}{25}} = \sqrt{\frac{425}{25}} = \sqrt{17}$$So, the absolute value of $\frac{z}{z-8}$ is $\sqrt{17}$.