Chapter 14, Problem 27E

To determine

To create:

• The complex variables $\text{c1}=1-3\text{i,}\text{c2}=5+2\text{i}$ and add them.

• The complex variables $\text{c1}=1-3\text{i,}\text{c2}=5+2\text{i}$ and multiply them.

• The complex variables $\text{c1}=1-3\text{i,}\text{c2}=5+2\text{i}$ and get the complex conjugate and magnitude of each.

• The complex variables $\text{c1}=1-3\text{i,}\text{c2}=5+2\text{i}$ and put them in polar form.

Answer to Problem 27E

Solution:

• The addition of $\text{c1}=1-3\text{i,}\text{c2}=5+2\text{i}$ gives $6-\text{i}$.

• The multiplication of $\text{c1}=1-3\text{i,}\text{c2}=5+2\text{i}$ gives $11-13\text{i}$.

• The complex conjugate and magnitude of $\text{c1}=1-3\text{i}$ is $1+3\text{i}$ and $3.16$, and for $\text{c2}=5+2\text{i}$ is $5-2\text{i}$ and $5.38$.

• The complex variables $\text{c1}=1-3\text{i,}\text{c2}=5+2\text{i}$ in polar form are stated as follows.

Explanation of Solution

• The complex variables $\text{c1}=1-3\text{i,}\text{c2}=5+2\text{i}$ and add them.

The given complex variables are,

$\text{c1}=1-3\text{i,}\text{c2}=5+2\text{i}$

Add them.

$\begin{array}{rll}\text{c1}+\text{c2}& =& 1-3\text{i}+\left(5+2\text{i}\right)\\ & =& 6-\text{i}\end{array}$

MATLAB Code:

a = 1-3*i;

%Define the variable a.

b = 5+2*i;

sum = a+b

Save the MATLAB function with name chapter1_54793_1_27_1E.m in the current folder. Execute the function by typing the function name at the command window to generate output.

Result:

Therefore, the result is stated above.

• The complex variables $\text{c1}=1-3\text{i,}\text{c2}=5+2\text{i}$ and multiply them.

The given complex variables are,

$\text{c1}=1-3\text{i,}\text{c2}=5+2\text{i}$

Multiply them.

$\begin{array}{rll}\text{c1}\times \text{c2}& =& \left(1-3\text{i}\right)\left(5+2\text{i}\right)\\ & =& 11-13\text{i}\end{array}$

MATLAB Code:

a = 1-3*i;

%Define the variable a.

b = 5+2*i;

Product = a*b

Save the MATLAB function with name chapter1_54793_1_27_2E.m in the current folder. Execute the function by typing the function name at the command window to generate output.

Result:

Therefore, the result is stated above.

• The complex variables $\text{c1}=1-3\text{i,}\text{c2}=5+2\text{i}$ and get the complex conjugate and magnitude of each.

The given complex variables are,

$\begin{array}{l}\text{c1}=1-3\text{i}\\ \text{c2}=5+2\text{i}\end{array}$

The complex conjugate of c1 is,

$\overline{\text{c1}}=1+3\text{i}$

The magnitude of c1 is,

$\begin{array}{rll}\left|\text{c}1\right|& =& \sqrt{1+3^2}\\ & =& 3.16\end{array}$

The complex conjugate of c2 is,

$\overline{\text{c2}}=5-2\text{i}$

The magnitude of c2 is,

$\begin{array}{rll}\left|\text{c2}\right|& =& \sqrt{5^2+2^2}\\ & =& 5.38\end{array}$

MATLAB Code:

a = 1-3*i;

%Define the variable a.

b = 5+2*i;

%Conjugate

conj(a)

conj(b)

%Magnitude

abs(a)

abs(b)

Save the MATLAB function with name chapter1_54793_1_27_3E.m in the current folder. Execute the function by typing the function name at the command window to generate output.

Result:

Therefore, the result is stated above.

• The complex variables $\text{c1}=1-3\text{i,}\text{c2}=5+2\text{i}$ and put them in polar form.

MATLAB Code:

a = 1-3*i;

%Define the variable a.

b = 5+2*i;

%polar form

r = abs(a)

theta = angle(a)

r = abs(b)

theta = angle(b)

Save the MATLAB function with name chapter1_54793_1_27_4E.m in the current folder. Execute the function by typing the function name at the command window to generate output.

Result:

Therefore, the result is stated above.