Chapter 9, Problem 18RE

To determine

To find: The complex number in standard form $a+bi$ .

Answer to Problem 18RE

The complex number in polar form of $z=0.10-0.02i$ is $\left(0.10,-0.02\right)$ .

Explanation of Solution

Given information:

The given polar equation is $0.1\left(\cos 350°+i\sin 350°\right)$ .

Calculation:

Calculate the x-coordinate of $0.1\left(\cos 350°+i\sin 350°\right)$ .

  $\begin{array}{c}x=r\cos \theta \\ =0.1\cos 350°\\ =0.1\cdot 1\\ =0.10\end{array}$

The y-coordinate is

  $\begin{array}{c}y=r\sin \theta \\ =0.1\sin 350°\\ =0.1\left(-0.2\right)\\ =-0.02\end{array}$

The z-coordinate is

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

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

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

The graph is plotted in the complex plane figure-(1) shows.

  

Figure-(1)

From the graph it is clear that the point is located in quadrant.

  $4^{th}$ .