Answer
$|-4+i|=\sqrt{17}$
Work Step by Step
The absolute value of a complex number
$z=a+bi,$ denoted $|z|,$ is a nonnegative
real number defined as $|z|=\sqrt{a^{2}+b^{2}}$.
$|z|=|-4+i|$
$=\sqrt{a^{2}+b^{2}}\qquad$ ...substitute $-4$ for $a$ and $1$ for $b$
$=\sqrt{(-4)^{2}+1^{2}}\qquad$ ...simplify.
$=\sqrt{16+1}$
$=\sqrt{17}$
