a. The absolute value of a complex number is its distance from the origin. If \(z=a+ bi\), then \(\displaystyle{\left|{z}\right|}={\left|{a}+{b}{i}\right|}=\sqrt{{{a}^{{2}}+{b}^{{2}}}}\)

The absolute value of a complex number \(z=5+12i\) is,

\(\displaystyle{\left|{z}\right|}={\left|{5}+{12}{i}\right|}=\sqrt{{{5}^{{2}}+{12}^{{2}}}}=\sqrt{{{25}+{144}}}=\sqrt{{169}}=\sqrt{{13}}\)

b. The absolute value of a complex number \(z=2−3i\) is,

\(\displaystyle{\left|{Z}\right|}={\left|{2}-{3}{i}\right|}=\sqrt{{{2}^{{2}}+{\left(-{3}\right)}^{{2}}}}=\sqrt{{{4}+{9}}}=\sqrt{{13}}\)