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

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

2021-02-10
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 $$\displaystyle\sqrt{{{5}}}$$.

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