Answer
$|4i|=4$
Work Step by Step
The absolute value of a complex number
$z=a+bi,$ denoted $|z|,$ is a nonnegative
real number defined as $|z|=\sqrt{a^{2}+b^{2}}$.
$|z|=|4i|$
$=\sqrt{a^{2}+b^{2}}\qquad$ ...substitute $0$ for $a$ and $4$ for $b$
$=\sqrt{0^{2}+4^{2}}\qquad$ ...simplify.
$=\sqrt{0+16}$
$=\sqrt{16}\qquad$ ...evaluate.
$=4$
