Q14P - Mathematical Methods in Physical Sciences

Question

Question: First simplify each of the following numbers to the x+iy form or to the $\mathit{r}{\mathit{e}}^{\mathbf{i}\mathbf{\theta }}$ form. Then plot the number in the complex plane.

$\mathbf{2}\mathbf{.}\mathbf{8}{\mathit{e}}^{\mathbf{-}\mathbf{i}\mathbf{(}\mathbf{1}\mathbf{.}\mathbf{1}\mathbf{)}}$ .

Step-by-Step Solution

Answer

The complex number can be written as z = 1.27 - 2.5i .

 

The graph is mentioned below:

Step 1: Given Information

The complex number is $2.8e^{-i(1.1)}$.

Step 2: Definition of the Complex number

A complex number is a number that consists of real and imaginary numbers and is written in the form as:

z=a+ib  where a and b are real, and z is the complex number.

Step 3: Find the values

The complex number is $2.8^{-i(1.1)}$ .

 

 $$\begin{gathered} r=2.8 \\ \theta =-1.1 \mathrm{rad} \\ =-63° \end{gathered}$$

The formula for x and y is given below.

 $$\begin{gathered} x=r \cos \left(\theta \right) \\ y=r \sin \left(\theta \right) \end{gathered}$$

 

Find x and y

 $$\begin{gathered} x=2.8\cos (-63°) \\ =1.27 \\ y=2.8\sin (-63°) \\ =-2.5 \\ z=1.27-2.5i \end{gathered}$$

 

The complex number can be written as $z=1.27-2.5i$.

 

The graph is mentioned below: