Chapter 6.5, Problem 9E

To determine

To find:the absolute value and plot the complex number.

Answer to Problem 9E

The absolute value $\left|z\right|=13.$

Explanation of Solution

Given:

  $\text{z=-5-12i}$

Concept used:

The absolute value or modulus of complex number is the distance between the origin $\left(0,0\right)$ and point $\left(\text{a,b}\right)$ in the complex plane.

Formula to find the absolute value of any complex number:

  $\left|\text{z}\right|\text{=}\sqrt{{\text{x}}^{\text{2}}{\text{+y}}^{\text{2}}}$ or $\left|\text{z}\right|\text{=}\sqrt{{\text{a}}^{\text{2}}{\text{+b}}^{\text{2}}}$ .

To plot the graph:

Step 1. Determine the real and imaginary party of the complex number.

Step2. Move along the horizontal axis to show the real part of the number.

Step3. Move parallel to the vertical to show the imaginary part of the number.

Step4. Plot the point.

Calculation:

The complex number is Interprets as $\text{z=a+bi}$ can be represent as the point $\left(\text{a,b}\right)$ in the complex plane.

The complex number $\text{z=-5-12i}$ can be represented as the point $\left(-5,-12\right)$ in the complex plane.

The plot complex number $\text{z=-5-12i}$ as shown in below:

  

The absolute value of $\text{z=a+bi}$ is $\left|\text{a+bi}\right|\text{=}\sqrt{{\text{a}}^{\text{2}}{\text{+b}}^{\text{2}}}$ .

  $\left|z\right|\text{=}\sqrt{{\left(-5\right)}^{\text{2}}\text{+}{\left(-12\right)}^{\text{2}}}$

  $\Rightarrow \sqrt{25+144}=13.$

Hence, the absolute value $\left|z\right|=13.$