Chapter 14, Problem 27E

Question

Want to see more full solutions like this?

Answer 1

Question

Chapter 14, Problem 27E

Expert Solution & Answer

To determine

To create:

• The complex variables c1=1−3i, c2=5+2i and add them.

• The complex variables c1=1−3i, c2=5+2i and multiply them.

• The complex variables c1=1−3i, c2=5+2i and get the complex conjugate and magnitude of each.

• The complex variables c1=1−3i, c2=5+2i and put them in polar form.

Answer to Problem 27E

Solution:

• The addition of c1=1−3i, c2=5+2i gives 6−i.

• The multiplication of c1=1−3i, c2=5+2i gives 11−13i.

• The complex conjugate and magnitude of c1=1−3i is 1+3i and 3.16, and for c2=5+2i is 5−2i and 5.38.

• The complex variables c1=1−3i, c2=5+2i in polar form are stated as follows.

Explanation of Solution

• The complex variables c1=1−3i, c2=5+2i and add them.

The given complex variables are,

c1=1−3i, c2=5+2i

Add them.

c1+c2=1−3i+(5+2i)=6−i

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:

MATLAB: A Practical Introduction to Programming and Problem Solving, Chapter 14, Problem 27E , additional homework tip 1

Therefore, the result is stated above.

• The complex variables c1=1−3i, c2=5+2i and multiply them.

The given complex variables are,

c1=1−3i, c2=5+2i

Multiply them.

c1×c2=(1−3i)(5+2i)=11−13i

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:

MATLAB: A Practical Introduction to Programming and Problem Solving, Chapter 14, Problem 27E , additional homework tip 2

Therefore, the result is stated above.

• The complex variables c1=1−3i, c2=5+2i and get the complex conjugate and magnitude of each.

The given complex variables are,

c1=1−3ic2=5+2i

The complex conjugate of c1 is,

c1¯=1+3i

The magnitude of c1 is,

|c1|=1+32=3.16

The complex conjugate of c2 is,

c2¯=5−2i

The magnitude of c2 is,

|c2|=52+22=5.38

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:

MATLAB: A Practical Introduction to Programming and Problem Solving, Chapter 14, Problem 27E , additional homework tip 3

Therefore, the result is stated above.

• The complex variables c1=1−3i, c2=5+2i 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:

MATLAB: A Practical Introduction to Programming and Problem Solving, Chapter 14, Problem 27E , additional homework tip 4

Therefore, the result is stated above.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Students have asked these similar questions

m Proctor ments sources Dak is investigating how long their phone's battery lasts (in hours) for various brightness levels (on a scale of 0-100). A part of the regression analysis done on Ti Calculator and in Excel for their data are displayed below. Ti Calculator Click this button to reveal the Ti Calculator Output. Click again to collapse it. Ti Calculator y = ax+b B0 and p 0 t = -3.02431335 p = 0.0233 df - 6 a =-0.0380555845 b=5.88809202 s = 0.436054238 20.603868129 r = -0.777089524 Resources Excel Type here to search Click this button to reveal the Excel Output. Click again to collapse it. SUMMARY OUTPUT Multiple R 0.777089524 R Square 0.603868129 Adjusted R Square 0.537846150 Standard Error 0.436054238 Observations 8 ANOVA df SS MS F Significance F Regression 1 1.73914021 Residual 6 1.14085979 1.73914021 0.190143298 9.1465 0.0233 Total 7 2.88000000 Coefficients Standard Error Intercept Brightness 5.88809202 -0.0380555845 t Stat 7.62593816 -3.02431335 P-value 0.0003 0.0233 Use…

ce Problems x + canvas.pdx.edu/courses/106252/assignments/1102408?module_item_id=4856656 m Proctor ments THIS IS THE second question of exdin where you have to Snow compere work to get run points. If you use TI calculator functions, you may write your work along with functions and values you I used and answers on a paper or type on an empty Word document or Excel file. If you use Ti calculator app on your computer or phone, you may provide screen shots of those on a word document or Excel file. Clearly provide the function along with values for the work. If you use Excel, you may use the Excel calculator or Excel as a calculator on your computer to provide complete work and the final answer on it. Please provide all the answers to the following questions on the same Excel sheet. If you use formula, you may write all your steps with numbers on a paper and submit a photo of it. Otherwise, you may type all those steps on a Word document or an Excel file. Do NOT round in the middle steps…

Suppose the model for certain data is a parabola y = Bo+B1x+B2x² with observations (1, 2.2), (2, 6.9), (3, 16.1), (4, 28.7), (5, 46.1). Describe the design matrix, the observation vector, and the parameter vector. Using these write down the system of equations to be approximated Xẞ = y, the parts of the normal equations XTX and XTy and write down the normal equations. Solve and determine the residual vector €. You may use a calculator for the computations but show the steps as described above.

Answer 2

Question

Chapter 14, Problem 27E

Expert Solution & Answer

To determine

To create:

• The complex variables c1=1−3i, c2=5+2i and add them.

• The complex variables c1=1−3i, c2=5+2i and multiply them.

• The complex variables c1=1−3i, c2=5+2i and get the complex conjugate and magnitude of each.

• The complex variables c1=1−3i, c2=5+2i and put them in polar form.

Answer to Problem 27E

Solution:

• The addition of c1=1−3i, c2=5+2i gives 6−i.

• The multiplication of c1=1−3i, c2=5+2i gives 11−13i.

• The complex conjugate and magnitude of c1=1−3i is 1+3i and 3.16, and for c2=5+2i is 5−2i and 5.38.

• The complex variables c1=1−3i, c2=5+2i in polar form are stated as follows.

Explanation of Solution

• The complex variables c1=1−3i, c2=5+2i and add them.

The given complex variables are,

c1=1−3i, c2=5+2i

Add them.

c1+c2=1−3i+(5+2i)=6−i

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:

MATLAB: A Practical Introduction to Programming and Problem Solving, Chapter 14, Problem 27E , additional homework tip 1

Therefore, the result is stated above.

• The complex variables c1=1−3i, c2=5+2i and multiply them.

The given complex variables are,

c1=1−3i, c2=5+2i

Multiply them.

c1×c2=(1−3i)(5+2i)=11−13i

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:

MATLAB: A Practical Introduction to Programming and Problem Solving, Chapter 14, Problem 27E , additional homework tip 2

Therefore, the result is stated above.

• The complex variables c1=1−3i, c2=5+2i and get the complex conjugate and magnitude of each.

The given complex variables are,

c1=1−3ic2=5+2i

The complex conjugate of c1 is,

c1¯=1+3i

The magnitude of c1 is,

|c1|=1+32=3.16

The complex conjugate of c2 is,

c2¯=5−2i

The magnitude of c2 is,

|c2|=52+22=5.38

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:

MATLAB: A Practical Introduction to Programming and Problem Solving, Chapter 14, Problem 27E , additional homework tip 3

Therefore, the result is stated above.

• The complex variables c1=1−3i, c2=5+2i 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:

MATLAB: A Practical Introduction to Programming and Problem Solving, Chapter 14, Problem 27E , additional homework tip 4

Therefore, the result is stated above.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Question

Chapter 14, Problem 27E

Expert Solution & Answer

To determine

To create:

• The complex variables c1=1−3i, c2=5+2i and add them.

• The complex variables c1=1−3i, c2=5+2i and multiply them.

• The complex variables c1=1−3i, c2=5+2i and get the complex conjugate and magnitude of each.

• The complex variables c1=1−3i, c2=5+2i and put them in polar form.

Answer to Problem 27E

Solution:

• The addition of c1=1−3i, c2=5+2i gives 6−i.

• The multiplication of c1=1−3i, c2=5+2i gives 11−13i.

• The complex conjugate and magnitude of c1=1−3i is 1+3i and 3.16, and for c2=5+2i is 5−2i and 5.38.

• The complex variables c1=1−3i, c2=5+2i in polar form are stated as follows.

Explanation of Solution

• The complex variables c1=1−3i, c2=5+2i and add them.

The given complex variables are,

c1=1−3i, c2=5+2i

Add them.

c1+c2=1−3i+(5+2i)=6−i

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:

MATLAB: A Practical Introduction to Programming and Problem Solving, Chapter 14, Problem 27E , additional homework tip 1

Therefore, the result is stated above.

• The complex variables c1=1−3i, c2=5+2i and multiply them.

The given complex variables are,

c1=1−3i, c2=5+2i

Multiply them.

c1×c2=(1−3i)(5+2i)=11−13i

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:

MATLAB: A Practical Introduction to Programming and Problem Solving, Chapter 14, Problem 27E , additional homework tip 2

Therefore, the result is stated above.

• The complex variables c1=1−3i, c2=5+2i and get the complex conjugate and magnitude of each.

The given complex variables are,

c1=1−3ic2=5+2i

The complex conjugate of c1 is,

c1¯=1+3i

The magnitude of c1 is,

|c1|=1+32=3.16

The complex conjugate of c2 is,

c2¯=5−2i

The magnitude of c2 is,

|c2|=52+22=5.38

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:

MATLAB: A Practical Introduction to Programming and Problem Solving, Chapter 14, Problem 27E , additional homework tip 3

Therefore, the result is stated above.

• The complex variables c1=1−3i, c2=5+2i 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:

MATLAB: A Practical Introduction to Programming and Problem Solving, Chapter 14, Problem 27E , additional homework tip 4

Therefore, the result is stated above.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Question

Chapter 14, Problem 27E

Expert Solution & Answer

To determine

To create:

• The complex variables c1=1−3i, c2=5+2i and add them.

• The complex variables c1=1−3i, c2=5+2i and multiply them.

• The complex variables c1=1−3i, c2=5+2i and get the complex conjugate and magnitude of each.

• The complex variables c1=1−3i, c2=5+2i and put them in polar form.

Answer to Problem 27E

Solution:

• The addition of c1=1−3i, c2=5+2i gives 6−i.

• The multiplication of c1=1−3i, c2=5+2i gives 11−13i.

• The complex conjugate and magnitude of c1=1−3i is 1+3i and 3.16, and for c2=5+2i is 5−2i and 5.38.

• The complex variables c1=1−3i, c2=5+2i in polar form are stated as follows.

Explanation of Solution

• The complex variables c1=1−3i, c2=5+2i and add them.

The given complex variables are,

c1=1−3i, c2=5+2i

Add them.

c1+c2=1−3i+(5+2i)=6−i

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:

MATLAB: A Practical Introduction to Programming and Problem Solving, Chapter 14, Problem 27E , additional homework tip 1

Therefore, the result is stated above.

• The complex variables c1=1−3i, c2=5+2i and multiply them.

The given complex variables are,

c1=1−3i, c2=5+2i

Multiply them.

c1×c2=(1−3i)(5+2i)=11−13i

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:

MATLAB: A Practical Introduction to Programming and Problem Solving, Chapter 14, Problem 27E , additional homework tip 2

Therefore, the result is stated above.

• The complex variables c1=1−3i, c2=5+2i and get the complex conjugate and magnitude of each.

The given complex variables are,

c1=1−3ic2=5+2i

The complex conjugate of c1 is,

c1¯=1+3i

The magnitude of c1 is,

|c1|=1+32=3.16

The complex conjugate of c2 is,

c2¯=5−2i

The magnitude of c2 is,

|c2|=52+22=5.38

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:

MATLAB: A Practical Introduction to Programming and Problem Solving, Chapter 14, Problem 27E , additional homework tip 3

Therefore, the result is stated above.

• The complex variables c1=1−3i, c2=5+2i 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:

MATLAB: A Practical Introduction to Programming and Problem Solving, Chapter 14, Problem 27E , additional homework tip 4

Therefore, the result is stated above.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Expert Solution & Answer

To determine

To create:

• The complex variables c1=1−3i, c2=5+2i and add them.

• The complex variables c1=1−3i, c2=5+2i and multiply them.

• The complex variables c1=1−3i, c2=5+2i and get the complex conjugate and magnitude of each.

• The complex variables c1=1−3i, c2=5+2i and put them in polar form.

Answer to Problem 27E

Solution:

• The addition of c1=1−3i, c2=5+2i gives 6−i.

• The multiplication of c1=1−3i, c2=5+2i gives 11−13i.

• The complex conjugate and magnitude of c1=1−3i is 1+3i and 3.16, and for c2=5+2i is 5−2i and 5.38.

• The complex variables c1=1−3i, c2=5+2i in polar form are stated as follows.

Explanation of Solution

• The complex variables c1=1−3i, c2=5+2i and add them.

The given complex variables are,

c1=1−3i, c2=5+2i

Add them.

c1+c2=1−3i+(5+2i)=6−i

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:

MATLAB: A Practical Introduction to Programming and Problem Solving, Chapter 14, Problem 27E , additional homework tip 1

Therefore, the result is stated above.

• The complex variables c1=1−3i, c2=5+2i and multiply them.

The given complex variables are,

c1=1−3i, c2=5+2i

Multiply them.

c1×c2=(1−3i)(5+2i)=11−13i

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:

MATLAB: A Practical Introduction to Programming and Problem Solving, Chapter 14, Problem 27E , additional homework tip 2

Therefore, the result is stated above.

• The complex variables c1=1−3i, c2=5+2i and get the complex conjugate and magnitude of each.

The given complex variables are,

c1=1−3ic2=5+2i

The complex conjugate of c1 is,

c1¯=1+3i

The magnitude of c1 is,

|c1|=1+32=3.16

The complex conjugate of c2 is,

c2¯=5−2i

The magnitude of c2 is,

|c2|=52+22=5.38

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:

MATLAB: A Practical Introduction to Programming and Problem Solving, Chapter 14, Problem 27E , additional homework tip 3

Therefore, the result is stated above.

• The complex variables c1=1−3i, c2=5+2i 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:

MATLAB: A Practical Introduction to Programming and Problem Solving, Chapter 14, Problem 27E , additional homework tip 4

Therefore, the result is stated above.

Answer 6

Expert Solution & Answer

To determine

To create:

• The complex variables c1=1−3i, c2=5+2i and add them.

• The complex variables c1=1−3i, c2=5+2i and multiply them.

• The complex variables c1=1−3i, c2=5+2i and get the complex conjugate and magnitude of each.

• The complex variables c1=1−3i, c2=5+2i and put them in polar form.

Answer to Problem 27E

Solution:

• The addition of c1=1−3i, c2=5+2i gives 6−i.

• The multiplication of c1=1−3i, c2=5+2i gives 11−13i.

• The complex conjugate and magnitude of c1=1−3i is 1+3i and 3.16, and for c2=5+2i is 5−2i and 5.38.

• The complex variables c1=1−3i, c2=5+2i in polar form are stated as follows.

Explanation of Solution

• The complex variables c1=1−3i, c2=5+2i and add them.

The given complex variables are,

c1=1−3i, c2=5+2i

Add them.

c1+c2=1−3i+(5+2i)=6−i

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:

MATLAB: A Practical Introduction to Programming and Problem Solving, Chapter 14, Problem 27E , additional homework tip 1

Therefore, the result is stated above.

• The complex variables c1=1−3i, c2=5+2i and multiply them.

The given complex variables are,

c1=1−3i, c2=5+2i

Multiply them.

c1×c2=(1−3i)(5+2i)=11−13i

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:

MATLAB: A Practical Introduction to Programming and Problem Solving, Chapter 14, Problem 27E , additional homework tip 2

Therefore, the result is stated above.

• The complex variables c1=1−3i, c2=5+2i and get the complex conjugate and magnitude of each.

The given complex variables are,

c1=1−3ic2=5+2i

The complex conjugate of c1 is,

c1¯=1+3i

The magnitude of c1 is,

|c1|=1+32=3.16

The complex conjugate of c2 is,

c2¯=5−2i

The magnitude of c2 is,

|c2|=52+22=5.38

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:

MATLAB: A Practical Introduction to Programming and Problem Solving, Chapter 14, Problem 27E , additional homework tip 3

Therefore, the result is stated above.

• The complex variables c1=1−3i, c2=5+2i 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:

MATLAB: A Practical Introduction to Programming and Problem Solving, Chapter 14, Problem 27E , additional homework tip 4

Therefore, the result is stated above.

Answer 7

Expert Solution & Answer

Answer 8

Expert Solution & Answer

Answer 9

To determine

To create:

• The complex variables c1=1−3i, c2=5+2i and add them.

• The complex variables c1=1−3i, c2=5+2i and multiply them.

• The complex variables c1=1−3i, c2=5+2i and get the complex conjugate and magnitude of each.

• The complex variables c1=1−3i, c2=5+2i and put them in polar form.

Answer 10

Answer to Problem 27E

Solution:

• The addition of c1=1−3i, c2=5+2i gives 6−i.

• The multiplication of c1=1−3i, c2=5+2i gives 11−13i.

• The complex conjugate and magnitude of c1=1−3i is 1+3i and 3.16, and for c2=5+2i is 5−2i and 5.38.

• The complex variables c1=1−3i, c2=5+2i in polar form are stated as follows.

Answer 11

Explanation of Solution

• The complex variables c1=1−3i, c2=5+2i and add them.

The given complex variables are,

c1=1−3i, c2=5+2i

Add them.

c1+c2=1−3i+(5+2i)=6−i

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:

MATLAB: A Practical Introduction to Programming and Problem Solving, Chapter 14, Problem 27E , additional homework tip 1

Therefore, the result is stated above.

• The complex variables c1=1−3i, c2=5+2i and multiply them.

The given complex variables are,

c1=1−3i, c2=5+2i

Multiply them.

c1×c2=(1−3i)(5+2i)=11−13i

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:

MATLAB: A Practical Introduction to Programming and Problem Solving, Chapter 14, Problem 27E , additional homework tip 2

Therefore, the result is stated above.

• The complex variables c1=1−3i, c2=5+2i and get the complex conjugate and magnitude of each.

The given complex variables are,

c1=1−3ic2=5+2i

The complex conjugate of c1 is,

c1¯=1+3i

The magnitude of c1 is,

|c1|=1+32=3.16

The complex conjugate of c2 is,

c2¯=5−2i

The magnitude of c2 is,

|c2|=52+22=5.38

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:

MATLAB: A Practical Introduction to Programming and Problem Solving, Chapter 14, Problem 27E , additional homework tip 3

Therefore, the result is stated above.

• The complex variables c1=1−3i, c2=5+2i 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:

MATLAB: A Practical Introduction to Programming and Problem Solving, Chapter 14, Problem 27E , additional homework tip 4

Therefore, the result is stated above.