Step 1

Absolute value of complex number \(\displaystyle{z}={a}+{i}{b}\) is represent by \(\displaystyle{\left|{z}\right|}\) and given as

\(\displaystyle{\left|{z}\right|}=\sqrt{{{\left({a}\right)}^{{{2}}}+{\left({b}\right)}^{{{2}}}}}\)

Step 2

Given complex number is

\(\displaystyle{z}={2}−{3}{i}\)

Step 3

\(\displaystyle{z}={2}+{\left(−{3}\right)}{i}\)

Here

\(\displaystyle{x}={2}{y}=−{3}\)

Now

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

\(\displaystyle=\sqrt{{{4}+{9}}}\)

\(\displaystyle=\sqrt{{{13}}}\)

Step 4

Answer:

Absolute value of complex number \(\displaystyle{2}−{3}{i}\) is \(\displaystyle\sqrt{{{13}}}\).

Absolute value of complex number \(\displaystyle{z}={a}+{i}{b}\) is represent by \(\displaystyle{\left|{z}\right|}\) and given as

\(\displaystyle{\left|{z}\right|}=\sqrt{{{\left({a}\right)}^{{{2}}}+{\left({b}\right)}^{{{2}}}}}\)

Step 2

Given complex number is

\(\displaystyle{z}={2}−{3}{i}\)

Step 3

\(\displaystyle{z}={2}+{\left(−{3}\right)}{i}\)

Here

\(\displaystyle{x}={2}{y}=−{3}\)

Now

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

\(\displaystyle=\sqrt{{{4}+{9}}}\)

\(\displaystyle=\sqrt{{{13}}}\)

Step 4

Answer:

Absolute value of complex number \(\displaystyle{2}−{3}{i}\) is \(\displaystyle\sqrt{{{13}}}\).