Chapter 9.6, Problem 15CFU

a.

To determine

To find: the magnitude of the force.

Answer to Problem 15CFU

The magnitude of the force is $18.02$ .

Explanation of Solution

Given information:

The complex number is $10+15i$ .

Calculation: to find magnitude of the force, first find the absolute value of the complex number

  $\begin{array}{l}\left|z\right|=\sqrt{{\left(10\right)}^2+{\left(15\right)}^2}\\ \left|z\right|=\sqrt{325}\text{ [square and add]}\\ \left|z\right|=18.02\text{ [simplify]}\end{array}$

Thus, the magnitude of the force is $18.02$ .

b.

To determine

To find: the direction of the force.

Answer to Problem 15CFU

The direction of the force is $\arctan \frac{5}{2}$ .

Explanation of Solution

Given information:

The complex number is $10+15i$ .

Calculation: to find direction of the force, use the formula and substitute,

  $\begin{array}{l}\theta =\arctan \frac{y}{x}\\ \theta =\arctan \frac{15}{10}\text{ [substitute]}\\ \theta =\arctan \frac{5}{2}\text{ [simplify]}\end{array}$

Thus, the direction of the force is $\arctan \frac{5}{2}$ .