Chapter 11, Problem 18RE

To determine

To find: The x-coordinates of $0.1\left(\cos 350°+i\sin 350°\right)$ .

Answer to Problem 18RE

The rectangular coordinates is $0.10-0.02i$ ..

Explanation of Solution

Given information:

The rectangular coordinates is $0.1\left(\cos 350°+i\sin 350°\right)$ .

Calculation:

Calculate the x-coordinates,

If $0.1\left(\cos 350°+i\sin 350°\right)$ represents a complex number in the polar form, then its $x$ and $y$ coordinates are $x=r\cos \theta$ and $y=r\sin \theta$ , where $\left(r,\theta \right)$ .

The x-coordinates of $0.1\left(\cos 350°+i\sin 350°\right)$ is,

  $\begin{array}{c}x=r\cos \theta \\ =0.1\cos 350°\\ =0.10\end{array}$

The y-coordinates is

  $\begin{array}{c}y=r\sin \theta \\ =0.1\sin 350°\\ =-0.02\end{array}$

  $\begin{array}{c}z=x+iy\\ =0.10-0.02i\end{array}$

Therefore, the rectangular form of $0.1\left(\cos 350°+i\sin 350°\right)$ is $0.10-0.02i$

The rectangular coordinates of the given point $z=0.10-0.02i$ are $\left(0.10-0.02i\right)$

The point is plotted in the complex plane figure-(1) shown .

  

Figure-(1)

Therefore, the rectangular coordinates is $0.10-0.02i$ ..