Question

# Determine the absolute value of the complex number 2 - 3i.

Piecewise-Defined Functions
Determine the absolute value of the complex number $$\displaystyle{2}-{3}{i}$$.

2020-11-11
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
Absolute value of complex number $$\displaystyle{2}−{3}{i}$$ is $$\displaystyle\sqrt{{{13}}}$$.