Answer
$|1-4i|=\sqrt{17}$
Work Step by Step
The plot of the given complex number, $ 1-4i ,$ is shown below.
The absolute value of the complex number $a+bi,$ written as $|a+bi|,$ is given by $\sqrt{a^2+b^2}.$ Therefore, the absolute value of the given complex number is \begin{align*} & \sqrt{(1)^2+(-4)^2} \\&= \sqrt{1+16} \\&= \sqrt{17} .\end{align*} Hence, $
|1-4i|=\sqrt{17}
.$
