Chapter 6 - Section 6.5 - Complex Numbers in Polar Form; DeMoivre's Theorem - Exercise Set - Page 767: 8

$$\sqrt{17}$$

We plot the complex number $z=4-i$ the same way we plot $(4,-1)$ in the rectangular coordinate system. We find the absolute value of the complex number as follows.$$|z|=|a+bi|=\sqrt{a^2+b^2} \\ \Rightarrow \quad |z|=|4+(-1)i|=\sqrt{4^2+(-1)^2}=\sqrt{17}$$