Assignment: Correcting Complex Number Polar Form
Part 1 – Who’s Right?
Each of the following problems has been answered by two students, Ying and Jabbar. In each
case, one of the student’s answers are correct, and the other student’s answers are incorrect.
For each question:
a. State which student’s response is correct.
b. Find, clearly identify, and correct the misconceptions in the incorrect student’s response.
c. Write 2-3 sentences describing the incorrect student’s mistakes and how it should be
corrected.
1. Express
3  i in polar form. Express all trigonometric values exactly.
Ying
Jabbar
z  3 i
r 
 3
z  3 i
2
 12  3  1  4  2
 3 
 1 
 
  arctan 
 3
 3  6
r 
 3
2
 12  3  1  4  2
 3 
 1 
 
  arctan 
 3
 3  6
  arctan 
  arctan 



z  2  cos  i sin 
6
6




z  2  sin  i cos 
6
6

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


2. Express 5  cos  i sin  in rectangular form. Express all trigonometric values exactly.
2
2

Ying
Jabbar



z  5  cos  i sin 
2
2

z  5 1  0i 



z  5  cos  i sin 
2
2

z  5  0  1i 
z  5
z  5i

 



3. Find the following product: 5  cos  i sin   2  cos  i sin  .
3
3
6
6

 
Express your final answer in rectangular form.
Ying
Jabbar

 



5  cos  i sin   2  cos  i sin 
3
3
6
6

 

 



5  cos  i sin   2  cos  i sin 
3
3
6
6

 

  
   
  5  2    cos     i sin    
3 6
 3 6 


  
   
  5  2    cos     i sin    
3 6
 3 6 




 3  cos  i sin 
2
2

 3  0  i 



 10  cos  i sin 
2
2

 10  0  i 
 3i
 10i
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4. Find the quotient of the following expressions:
5
5 




7  cos
 i sin
 2  cos  i sin  .Express your final answer in rectangular form.
6
6 
2
2


Ying
Jabbar
5
5

7  cos
 i sin
6
6






  2  cos 2  i sin 2 



7 
 5  
 5   
   i sin 
 
 cos 
2 
 6 2
 6 2 
5
5

7  cos
 i sin
6
6


2 
  5
 cos  
7 
2 6




  2  cos  i sin 
2
2



  5  
  i sin  2  6  



7


   cos  i sin 
2
3
3
7
 
  
   cos     i sin    
2
 3
 3 
71
3 
  
i

2  2 2 
71
3 
  
i

2  2 2 

7 7 3

i
4
4

7 7 3

i
4
4
Part 2 – Common Mistakes
The problems above describe some of the most common mistakes made when first working with
the polar form of complex numbers.
Which of the mistakes described do you find the easiest to make? Write 4-5 sentences that
describe what you feel is the most common type of mistake made. In your response be sure to
include the following:



Describe the mistake.
Explain why you find the mistake easiest to make.
What steps can you take to help you avoid these types of mistakes in the future?
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