Determine the absolute value of each of the following complex numbers: a. z = 3 + 4i b. z = -1 - 2i.

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:
${\displaystyle \left|z\right|=\sqrt{{(-1)}^2+{(-2)}^2}}$
${\displaystyle =\sqrt{5}}$
Hence, absolute value is ${\displaystyle \sqrt{5}}$.