Step 1

To find the absolute value of the given complex numbers.

a. Given complex number is z=3+4i

Absolute value of a complex number is the distance of complex number from origin.

It is given by \(\displaystyle{\left|{\left|{z}\right|}\right|}\)

Absolute value of the given complex number will be:

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

\(\displaystyle=\sqrt{{{25}}}\)

=5

Step 2

b. Given complex number is z=−1−2i

Absolute value of given complex number will be:

\(\displaystyle{\left|{{z}}\right|}=\sqrt{{{\left(-{1}\right)}^{{2}}+{\left(-{2}\right)}^{{2}}}}\)

\(\displaystyle=\sqrt{{{5}}}\)

Hence, absolute value is \(\displaystyle\sqrt{{{5}}}\).

To find the absolute value of the given complex numbers.

a. Given complex number is z=3+4i

Absolute value of a complex number is the distance of complex number from origin.

It is given by \(\displaystyle{\left|{\left|{z}\right|}\right|}\)

Absolute value of the given complex number will be:

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

\(\displaystyle=\sqrt{{{25}}}\)

=5

Step 2

b. Given complex number is z=−1−2i

Absolute value of given complex number will be:

\(\displaystyle{\left|{{z}}\right|}=\sqrt{{{\left(-{1}\right)}^{{2}}+{\left(-{2}\right)}^{{2}}}}\)

\(\displaystyle=\sqrt{{{5}}}\)

Hence, absolute value is \(\displaystyle\sqrt{{{5}}}\).