Step 1:To determine

Plot the complex number \(z=−3−4i\) and find its absolute value.

Step 2:Calculation

The given complex number \(z=−3−4i\) can be plotted as the cooordinate \((−3,−4)\) on the x-y plane.

So, the complex number is plotted as:

Consider the complex number \(z=x+iy\).

The absolute value is given by:

\(\displaystyle{\left|{z}\right|}=\sqrt{{{x}^{{{2}}}+{y}^{{{2}}}}}\)

Consider the given complex number \(z=−3−4i\)

So, the absolute value is given by:

\(\displaystyle{\left|{z}\right|}=\sqrt{{{\left(-{3}\right)}^{{{2}}}+{\left(-{4}\right)}^{{{2}}}}}\)

\(\displaystyle\Rightarrow{\left|{z}\right|}=\sqrt{{{9}+{16}}}\)

\(\displaystyle\Rightarrow{\left|{z}\right|}=\sqrt{{{25}}}\)

\(\displaystyle\Rightarrow{\left|{z}\right|}={5}\)