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

Determine the absolute value of each of the following complex numbers:
a. z = 3 + 4i
b. z = -1 - 2i.
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Ezra Herbert
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 $||z||$
Absolute value of the given complex number will be:
$|z|=\sqrt{{\left(3\right)}^{2}+{\left(4\right)}^{2}}$
$=\sqrt{25}$
=5
Step 2
b. Given complex number is z=−1−2i
Absolute value of given complex number will be:
$|z|=\sqrt{{\left(-1\right)}^{2}+{\left(-2\right)}^{2}}$
$=\sqrt{5}$
Hence, absolute value is $\sqrt{5}$.