Step 1

The given expression is 4i.

The Cartesian point in complex plane is (0,4).

The graph is shown below:

Step 2

The distance formula for points on the Cartesian plane:\(\displaystyle{d}=\sqrt{{{\left({x}_{{{2}}}-{x}_{{{1}}}\right)}^{{{2}}}+{\left({y}_{{{2}}}-{y}_{{{1}}}\right)}^{{{2}}}}}\).

\(\displaystyle{d}=\sqrt{{{\left({0}-{0}\right)}^{{{2}}}+{\left({0}-{4}\right)}^{{{2}}}}}\)

\(\displaystyle=\sqrt{{{0}+{16}}}\)

=4

The absolute value of the number 4i is 4.