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STPM Coursework

STPM 2018 Term 1 Mathematics (T) Coursework Sample

By KK LEE

August 20, 2017

STPM 2018 Term 1 Mathematics (T) Coursework PBS Assignment

STPM Coursework Sample Solution

Question

A complex number is an extension of a real number and it can be represented in Cartesian and polar
forms. In this assignment, you are required to explore the powers and roots of complex numbers.

(a) Let z =1+i. Find z^n, where n = 2, 3, 4, …, and represent the complex numbers on an Argand diagram.
(b) Rewrite z=1+i in polar form and repeat task (a).
(c) Comment on the methods used in (a) and (b).

2 Let z=r(cos pi/5+isin pi/5). Find z^n, where n = 2, 3, 4, …, with a value of r in each of the following cases:
(a) 0 (b) r>1.
Represent the complex numbers on an Argand diagram and comment on your results.

3. Find the n complex numbers which satisfy the equation z^n=a+bi, for n>3 and represent them on an Argand diagram in each of the following cases:
(a) a<>0, b=0,
(b) a=0, b<>0,
(c) a<>0, b<>0.
State the conjugate pairs of the roots, if any.

Solution

Please check with your teacher for all the requirements. All sample below are for reference only.

Question 1 (a)

Question 1 (b)

Question 1 (c)

Both methods (a) and (b) are suitable for small value of n when finding z^n. For n is large, polar form will be more suitable to explore the power of complex numbers. Actually polar form is more suitable to find powers of complex number because of the de Moivre’s theorem. We can express z^n easily by using de Moivre’s theorem.

Question 2 (a)

Modulus of z^n decrease as n increase. Each higher power is pi/5 rad further along and closer to 0. Five powers are displayed. It forms a spiral and this spiral is called an exponential spiral.

Question 2 (b)

Modulus of z^n increases as n increase. Each higher power is pi/5 rad further along and further to 0. Five powers are displayed. It forms a spiral and this spiral is called an exponential spiral.

Question 3 (a)

You can try to modify the value of b. Example, use b<0, or any other numbers.

Extra sample of Argand digram with n=6 and n=7

Question 3 (b)

You can try to modify the value of a. Example, use a<0, or any other numbers.

Extra sample of Argand digram with n=6 and n=7

Question 3 (c)

You can try to modify the values of a and b. Example, use a<0, b>0 or any other numbers.

Extra sample of Argand digram with n=6 and n=7

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70 Comments

Shirley on August 21, 2017 at 9:13 pm

Nice work! Thank you!
Reply
- KK LEE on September 7, 2017 at 12:52 am
  
  You are welcome
- Rajiv Kumar on March 24, 2020 at 1:27 pm
  
  Nice work and it’s very important to all
  ….
  Thank and Regards.
David on August 24, 2017 at 5:59 am

How to plot the argand diagram using computer? Can you please teach me??
Reply
- KK LEE on September 7, 2017 at 12:52 am
  
  Geogebra
genevieve on August 24, 2017 at 4:58 pm

thank you so much
Reply
- KK LEE on September 7, 2017 at 12:52 am
  
  You are welcome
LEE on August 28, 2017 at 7:02 pm

how to draw the Argand diagram for Q3C in details?
Reply
- KK LEE on September 7, 2017 at 12:52 am
  
  You are welcome
Erica on August 28, 2017 at 8:41 pm

it helps me a lot ! thanks!
Reply
- KK LEE on September 7, 2017 at 12:51 am
  
  You are welcome
Maths lover on September 1, 2017 at 11:27 pm

Sir, I am curious about what program did you used to plot the graph? May you share it with us? Thank in advance Sir.
Reply
- KK LEE on September 7, 2017 at 12:51 am
  
  Geogebra
hugo on September 2, 2017 at 2:05 am

may i know roughly how to draw the graphs for question 3?
Reply
- KK LEE on September 7, 2017 at 12:51 am
  
  Geogebra
Jason on September 4, 2017 at 1:35 pm

Um sir. May I know which app or software you use to plot those Argand diagrams?
Reply
- KK LEE on September 7, 2017 at 12:49 am
  
  Geogebra
yee on September 4, 2017 at 9:29 pm

Thanks
Reply
- KK LEE on September 7, 2017 at 12:49 am
  
  You are welcome
yamid on September 6, 2017 at 8:00 pm

Sir,do the points in 2 a and 2b need to connect together?
Reply
- KK LEE on September 7, 2017 at 12:48 am
  
  It depends on your teacher.
- KANG CHUANG HSIEN on September 14, 2017 at 8:40 am
  
  Sir, can I ask the methodology and results is seperated?
Nicole on September 6, 2017 at 10:12 pm

thanks! definitely a great reference
Reply
- KK LEE on September 7, 2017 at 12:51 am
  
  You are welcome.
TM on September 7, 2017 at 8:28 pm

Sir,how to do methodology??
Tq
Reply
- KK LEE on September 17, 2017 at 10:02 pm
  
  Please check with your school teacher for methodology. This page shows the result only.
Freddy on September 7, 2017 at 8:53 pm

How to plot the graph in 1B question?
Reply
- KK LEE on September 17, 2017 at 10:03 pm
  
  Geogebra
CJoanne on September 7, 2017 at 10:41 pm

Thank you soooo much!
This is the only website that I can refer from and it is very useful 🙂
I’ll search for this website again for the next coming sem math t assignment 🙂
Really appreciate your effort to upload the answer T T
Reply
low on September 8, 2017 at 8:11 pm

Hi ,can I know how to use geogebra
Reply
- KK LEE on September 17, 2017 at 10:03 pm
  
  https://wiki.geogebra.org/en/Manual
chenli on September 9, 2017 at 1:33 pm

sorry sir can i know about how to plot question 1 in spiral shape?
Reply
- KK LEE on September 17, 2017 at 10:04 pm
  
  You can use geogebra or use paper. It depends on your school teacher
feicheng on September 9, 2017 at 1:33 pm

sorry sir can i ask about how to plot question 1 in spiral shape
Reply
Renuga on September 10, 2017 at 5:11 pm

How to write introduction and methodology?
Reply
- KK LEE on September 17, 2017 at 10:05 pm
  
  Please check with your school teacher for methodology and intro. This page shows the result only.
ericalow on September 11, 2017 at 9:56 pm

great guidelines for the candidates ! thanks!
Reply
- KK LEE on September 17, 2017 at 10:05 pm
  
  You are welcome
choo on September 13, 2017 at 11:40 pm

sir lee
may i ask how to put methodology in our assignment?
Reply
- KK LEE on September 17, 2017 at 10:05 pm
  
  Please check with your school teacher for methodology. This page shows the result only.
KANG CHUANG HSIEN on September 14, 2017 at 8:40 am

Sir, can I ask the methodology and results is seperated?
Reply
- KK LEE on September 17, 2017 at 10:05 pm
  
  Yes
Megan on September 16, 2017 at 10:00 pm

Sir,may I know how to write a methodology?
Reply
- KK LEE on September 17, 2017 at 10:05 pm
  
  Please check with your school teacher for methodology. This page shows the result only.
ong on September 17, 2017 at 9:41 pm

how to write methodology?
Reply
- KK LEE on September 17, 2017 at 10:06 pm
  
  Please check with your school teacher for methodology. This page shows the result only.
cheang on September 20, 2017 at 3:30 pm

z^n=(-1)^k(2)^2k n=4k
(-1)^k(2)^2k(1+i) n=4k+1

please guide me about where does the solution
come from?
(-1)^k(2)^2k?
Reply
- cheang on September 20, 2017 at 3:33 pm
  
  anyway im from penang
- KK LEE on September 25, 2017 at 11:53 am
  
  From observation.
  
  It is like 2=x, if you call x=2, or 2=2x, if you call x=1. It depends on how you define it. you can write any expression if your teacher wants it.
KJ on October 1, 2017 at 1:39 pm

thank you very much!!
Reply
Naqe' on October 8, 2017 at 7:17 pm

Sir, can you teach how to do the viva?
Reply
Liew Zheng Hao on October 11, 2017 at 9:26 pm

Sir graph for ques 1a can be in spiral shape?
Reply
- KK LEE on October 22, 2017 at 8:36 pm
  
  Yes
- KK LEE on October 22, 2017 at 8:37 pm
  
  Yes. You can
priya on October 12, 2017 at 9:54 am

Sir how to do 1)b) repeat the task?
Reply
- KK LEE on October 22, 2017 at 8:37 pm
  
  Redo the power 2, 3, 4, 5
Soo Seok Huey on October 18, 2017 at 6:56 pm

Sir can i know how to connect those points become an exponential spiral?
Reply
- KK LEE on October 22, 2017 at 8:38 pm
  
  Using Computer? Or manual?
Yew on October 21, 2017 at 9:43 pm

May i know is the 3c’s argond diagram same as the 3b? *hand drawing
Reply
- KK LEE on October 22, 2017 at 8:38 pm
  
  The roots are different
Yugesha on October 27, 2017 at 6:16 pm

Sir how to plot the graph and draw the diagrams?
Reply
- KK LEE on October 28, 2017 at 12:34 am
  
  You can use geogebra to draw it. Download it and install in your computer or phone
cash on January 15, 2018 at 8:56 pm

Semester 2 coursework answer when published???
Reply
- KK LEE on January 17, 2018 at 10:40 pm
  
  It will be published if they are available
- cash on May 27, 2018 at 11:06 pm
  
  When can i get semester 3 coursework results??
Lim on January 19, 2018 at 7:13 pm

Hi sir, can I know what is the conjugate pair for 3(a) when n=6
Reply
- KK LEE on January 24, 2018 at 1:28 pm
  
  Conjugate for x+yi is x-yi. If you have the first complex root is 2+3i, then the second root will be 2-3i
Michael Hii on May 3, 2018 at 10:09 pm

math is too difficult to me even I do more exercise , how I should do to master every chapter
Reply
- KK LEE on May 14, 2018 at 11:50 pm
  
  Please find a good teacher to guide you
cash on May 27, 2018 at 11:04 pm

When can i get semester 3 coursework results??
Reply

Submit a Comment Cancel reply

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Tags: Complex Numbers de Moivre Theorem MT Term 1 STPM 2018 STPM MT

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KK LEE

KK LEE has been a STPM Mathematics tuition teacher since June 2006, but his love of Maths dates back to at least 1999 when he was Form 4. KK LEE started teaching in 2006 at Pusat Tuisyen Kasturi. He was known as "LK" when he was teaching in PTK. After teaching STPM Mathematics for 8 years in PTK, he joined Ai Tuition Centre in 2014. Over the years he has taught Mathematics (T), Mathematics (S), Mathematics (M), Additional Mathematics.

70 Comments

Shirley on August 21, 2017 at 9:13 pm

Nice work! Thank you!
Reply
- KK LEE on September 7, 2017 at 12:52 am
  
  You are welcome
- Rajiv Kumar on March 24, 2020 at 1:27 pm
  
  Nice work and it’s very important to all
  ….
  Thank and Regards.
David on August 24, 2017 at 5:59 am

How to plot the argand diagram using computer? Can you please teach me??
Reply
- KK LEE on September 7, 2017 at 12:52 am
  
  Geogebra
genevieve on August 24, 2017 at 4:58 pm

thank you so much
Reply
- KK LEE on September 7, 2017 at 12:52 am
  
  You are welcome
LEE on August 28, 2017 at 7:02 pm

how to draw the Argand diagram for Q3C in details?
Reply
- KK LEE on September 7, 2017 at 12:52 am
  
  You are welcome
Erica on August 28, 2017 at 8:41 pm

it helps me a lot ! thanks!
Reply
- KK LEE on September 7, 2017 at 12:51 am
  
  You are welcome
Maths lover on September 1, 2017 at 11:27 pm

Sir, I am curious about what program did you used to plot the graph? May you share it with us? Thank in advance Sir.
Reply
- KK LEE on September 7, 2017 at 12:51 am
  
  Geogebra
hugo on September 2, 2017 at 2:05 am

may i know roughly how to draw the graphs for question 3?
Reply
- KK LEE on September 7, 2017 at 12:51 am
  
  Geogebra
Jason on September 4, 2017 at 1:35 pm

Um sir. May I know which app or software you use to plot those Argand diagrams?
Reply
- KK LEE on September 7, 2017 at 12:49 am
  
  Geogebra
yee on September 4, 2017 at 9:29 pm

Thanks
Reply
- KK LEE on September 7, 2017 at 12:49 am
  
  You are welcome
yamid on September 6, 2017 at 8:00 pm

Sir,do the points in 2 a and 2b need to connect together?
Reply
- KK LEE on September 7, 2017 at 12:48 am
  
  It depends on your teacher.
- KANG CHUANG HSIEN on September 14, 2017 at 8:40 am
  
  Sir, can I ask the methodology and results is seperated?
Nicole on September 6, 2017 at 10:12 pm

thanks! definitely a great reference
Reply
- KK LEE on September 7, 2017 at 12:51 am
  
  You are welcome.
TM on September 7, 2017 at 8:28 pm

Sir,how to do methodology??
Tq
Reply
- KK LEE on September 17, 2017 at 10:02 pm
  
  Please check with your school teacher for methodology. This page shows the result only.
Freddy on September 7, 2017 at 8:53 pm

How to plot the graph in 1B question?
Reply
- KK LEE on September 17, 2017 at 10:03 pm
  
  Geogebra
CJoanne on September 7, 2017 at 10:41 pm

Thank you soooo much!
This is the only website that I can refer from and it is very useful 🙂
I’ll search for this website again for the next coming sem math t assignment 🙂
Really appreciate your effort to upload the answer T T
Reply
low on September 8, 2017 at 8:11 pm

Hi ,can I know how to use geogebra
Reply
- KK LEE on September 17, 2017 at 10:03 pm
  
  https://wiki.geogebra.org/en/Manual
chenli on September 9, 2017 at 1:33 pm

sorry sir can i know about how to plot question 1 in spiral shape?
Reply
- KK LEE on September 17, 2017 at 10:04 pm
  
  You can use geogebra or use paper. It depends on your school teacher
feicheng on September 9, 2017 at 1:33 pm

sorry sir can i ask about how to plot question 1 in spiral shape
Reply
Renuga on September 10, 2017 at 5:11 pm

How to write introduction and methodology?
Reply
- KK LEE on September 17, 2017 at 10:05 pm
  
  Please check with your school teacher for methodology and intro. This page shows the result only.
ericalow on September 11, 2017 at 9:56 pm

great guidelines for the candidates ! thanks!
Reply
- KK LEE on September 17, 2017 at 10:05 pm
  
  You are welcome
choo on September 13, 2017 at 11:40 pm

sir lee
may i ask how to put methodology in our assignment?
Reply
- KK LEE on September 17, 2017 at 10:05 pm
  
  Please check with your school teacher for methodology. This page shows the result only.
KANG CHUANG HSIEN on September 14, 2017 at 8:40 am

Sir, can I ask the methodology and results is seperated?
Reply
- KK LEE on September 17, 2017 at 10:05 pm
  
  Yes
Megan on September 16, 2017 at 10:00 pm

Sir,may I know how to write a methodology?
Reply
- KK LEE on September 17, 2017 at 10:05 pm
  
  Please check with your school teacher for methodology. This page shows the result only.
ong on September 17, 2017 at 9:41 pm

how to write methodology?
Reply
- KK LEE on September 17, 2017 at 10:06 pm
  
  Please check with your school teacher for methodology. This page shows the result only.
cheang on September 20, 2017 at 3:30 pm

z^n=(-1)^k(2)^2k n=4k
(-1)^k(2)^2k(1+i) n=4k+1

please guide me about where does the solution
come from?
(-1)^k(2)^2k?
Reply
- cheang on September 20, 2017 at 3:33 pm
  
  anyway im from penang
- KK LEE on September 25, 2017 at 11:53 am
  
  From observation.
  
  It is like 2=x, if you call x=2, or 2=2x, if you call x=1. It depends on how you define it. you can write any expression if your teacher wants it.
KJ on October 1, 2017 at 1:39 pm

thank you very much!!
Reply
Naqe' on October 8, 2017 at 7:17 pm

Sir, can you teach how to do the viva?
Reply
Liew Zheng Hao on October 11, 2017 at 9:26 pm

Sir graph for ques 1a can be in spiral shape?
Reply
- KK LEE on October 22, 2017 at 8:36 pm
  
  Yes
- KK LEE on October 22, 2017 at 8:37 pm
  
  Yes. You can
priya on October 12, 2017 at 9:54 am

Sir how to do 1)b) repeat the task?
Reply
- KK LEE on October 22, 2017 at 8:37 pm
  
  Redo the power 2, 3, 4, 5
Soo Seok Huey on October 18, 2017 at 6:56 pm

Sir can i know how to connect those points become an exponential spiral?
Reply
- KK LEE on October 22, 2017 at 8:38 pm
  
  Using Computer? Or manual?
Yew on October 21, 2017 at 9:43 pm

May i know is the 3c’s argond diagram same as the 3b? *hand drawing
Reply
- KK LEE on October 22, 2017 at 8:38 pm
  
  The roots are different
Yugesha on October 27, 2017 at 6:16 pm

Sir how to plot the graph and draw the diagrams?
Reply
- KK LEE on October 28, 2017 at 12:34 am
  
  You can use geogebra to draw it. Download it and install in your computer or phone
cash on January 15, 2018 at 8:56 pm

Semester 2 coursework answer when published???
Reply
- KK LEE on January 17, 2018 at 10:40 pm
  
  It will be published if they are available
- cash on May 27, 2018 at 11:06 pm
  
  When can i get semester 3 coursework results??
Lim on January 19, 2018 at 7:13 pm

Hi sir, can I know what is the conjugate pair for 3(a) when n=6
Reply
- KK LEE on January 24, 2018 at 1:28 pm
  
  Conjugate for x+yi is x-yi. If you have the first complex root is 2+3i, then the second root will be 2-3i
Michael Hii on May 3, 2018 at 10:09 pm

math is too difficult to me even I do more exercise , how I should do to master every chapter
Reply
- KK LEE on May 14, 2018 at 11:50 pm
  
  Please find a good teacher to guide you
cash on May 27, 2018 at 11:04 pm

When can i get semester 3 coursework results??
Reply

Submit a Comment Cancel reply

This site uses Akismet to reduce spam. Learn how your comment data is processed.

STPM 2018 Term 1 Mathematics (T) Coursework Sample

By KK LEE

STPM 2018 Term 1 Mathematics (T) Coursework PBS Assignment

Question

Solution

Question 1 (a)

Question 1 (b)

Question 1 (c)

Question 2 (a)

Question 2 (b)

Question 3 (a)

Question 3 (b)

Question 3 (c)

KK LEE

Dont wait

Learn More About My Mathematics Tuition. Try Out The Classes Today.

70 Comments

Submit a Comment Cancel reply

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Have a great day!

KK LEE

70 Comments

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