# one way that complex numbers are used is as abstract

August 30, 2017

one way that complex numbers are used is as abstract quantities to give understandable solutions to calculations. The polar form of a complex number describes the number’s magnitude and angle.

Follow the directions outlined in the project guide.

For this assignment you will evaluate student responses to questions about the polar form of complex numbers. In each problem you will be presented with two student responses to the question. One response is correct and the other response is incorrect. You will identify the correct response, and provide feedback to the incorrect student in correcting their answer.

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 6

3

r

3

2

12 3 1 4 2

3
1

arctan
3 6

3

arctan

arctan

z 2 cos i sin
6
6

z 2 sin i cos
6
6

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

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

4. Find the quotient of the following expressions:
5
5

7 cos
i sin
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

71
3

i
2 2

2

71
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?