Chapter 6.5, Problem 18E

To determine

To plot and find the absolute value of the complex number $5-12i$ .

Answer to Problem 18E

13

Explanation of Solution

Given:

Given complex number: $5-12i$

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:

  $\Rightarrow 5-12i$

Writing the above complex number in coordinate form,

  $\Rightarrow (5,-12)$

Graph:

  

2. Calculation of absolute value:

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

  $\begin{array}{l}|5-12i|=|(5)+(-12)i|\\ =\sqrt{{(5)}^2+{(-12)}^2}\\ =\sqrt{25+144}\\ =\sqrt{169}\\ =13\end{array}$

Conclusion:

Therefore, the absolute value of given complex number is equal to 13.