Chapter 6, Problem 9PS

a.

To determine

The solution of the roots in trigonometric form.

Answer to Problem 9PS

  $2(\cos {30}^o+i\sin {30}^o)$ , $2(\cos {150}^o+i\sin {150}^o)$ and $2(\cos {270}^o+i\sin {270}^o)$ .

Explanation of Solution

Given information:

For each graph of the roots of a complex number, write each of the roots in trigonometric form.

  

Calculation:

From the given information, the graph shows the starting clockwise from positive real axis, the roots would be as follows:

  $2(\cos {30}^o+i\sin {30}^o)$

  $2(\cos {150}^o+i\sin {150}^o)$

  $2(\cos {270}^o+i\sin {270}^o)$

The roots in trigonometric form are shown below:

  

Thus, the roots are $2(\cos {30}^o+i\sin {30}^o)$ , $2(\cos {150}^o+i\sin {150}^o)$ and $2(\cos {270}^o+i\sin {270}^o)$ .

b.

To determine

The solution of the roots in trigonometric form.

Answer to Problem 9PS

  $3(\cos {45}^o+i\sin {45}^o)$ , $3(\cos {135}^o+i\sin {135}^o)$ , $3(\cos {225}^o+i\sin {225}^o)$ and $3(\cos {315}^o+i\sin {315}^o)$ .

Explanation of Solution

Given information:

For each graph of the roots of a complex number, write each of the roots in trigonometric form.

  

Calculation:

From the given information, the graph shows the starting clockwise from positive real axis, the roots would be as follows:

  $3(\cos {45}^o+i\sin {45}^o)$

  $3(\cos {135}^o+i\sin {135}^o)$

  $3(\cos {225}^o+i\sin {225}^o)$

  $3(\cos {315}^o+i\sin {315}^o)$

The roots in trigonometric form are shown below:

  

Thus, the roots are $3(\cos {45}^o+i\sin {45}^o)$ , $3(\cos {135}^o+i\sin {135}^o)$ , $3(\cos {225}^o+i\sin {225}^o)$ and $3(\cos {315}^o+i\sin {315}^o)$ .