Chapter 6.5, Problem 16E

To determine

To plot and find the absolute value of the complex number $-7$ .

Answer to Problem 16E

  $7$

Explanation of Solution

Given:

Given complex number: $-7$

Concept used:

The absolute value of a complex number $a+bi$ is nothing but the distance between the origin

(0, 0) and the point $(a,b)$ in the complex plane.

  $|a+bi|=\sqrt{a^2+b^2}$

Calculation:

1. Plotting the given complex number:

  $\begin{array}{l}\Rightarrow -7\\ \Rightarrow -7+0i\end{array}$

Writing the above complex number in coordinate form,

  $\Rightarrow (-7,0)$

Graph:

  

2. Calculation of absolute value:

By using above concept, the absolute value of given complex number is,

  $\begin{array}{l}|-7+0i|=|(-7)+(0)i|\\ =\sqrt{{(-7)}^2+{(0)}^2}\\ =\sqrt{49+0}\\ =\sqrt{49}\\ =7\end{array}$

Conclusion:

Therefore, the absolute value of given complex number is equal to $7$ .