Question

Plot the complex number z = -3 - 4i and find its absolute value.

Piecewise-Defined Functions
ANSWERED
asked 2021-09-08

Plot the complex number \(z = -3 - 4i\) and find its absolute value.

Expert Answers (1)

2021-09-09

Step 1:To determine
Plot the complex number \(z=−3−4i\) and find its absolute value.
Step 2:Calculation
The given complex number \(z=−3−4i\) can be plotted as the cooordinate \((−3,−4)\) on the x-y plane.
So, the complex number is plotted as:
image
Consider the complex number \(z=x+iy\).
The absolute value is given by:
\(\displaystyle{\left|{z}\right|}=\sqrt{{{x}^{{{2}}}+{y}^{{{2}}}}}\)
Consider the given complex number \(z=−3−4i\)
So, the absolute value is given by:
\(\displaystyle{\left|{z}\right|}=\sqrt{{{\left(-{3}\right)}^{{{2}}}+{\left(-{4}\right)}^{{{2}}}}}\)
\(\displaystyle\Rightarrow{\left|{z}\right|}=\sqrt{{{9}+{16}}}\)
\(\displaystyle\Rightarrow{\left|{z}\right|}=\sqrt{{{25}}}\)
\(\displaystyle\Rightarrow{\left|{z}\right|}={5}\)

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