STPM 2018 Term 1 Mathematics (T) Coursework PBS Assignment
STPM Coursework Sample SolutionQuestion
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.
1
(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
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)
Question 2 (a)
Question 2 (b)
Question 3 (a)
You can try to modify the value of b. Example, use b<0, or any other numbers.
Question 3 (b)
You can try to modify the value of a. Example, use a<0, or any other numbers.
Question 3 (c)
You can try to modify the values of a and b. Example, use a<0, b>0 or any other numbers.
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Nice work! Thank you!
You are welcome
Nice work and it’s very important to all
….
Thank and Regards.
How to plot the argand diagram using computer? Can you please teach me??
Geogebra
thank you so much
You are welcome
how to draw the Argand diagram for Q3C in details?
You are welcome
it helps me a lot ! thanks!
You are welcome
Sir, I am curious about what program did you used to plot the graph? May you share it with us? Thank in advance Sir.
Geogebra
may i know roughly how to draw the graphs for question 3?
Geogebra
Um sir. May I know which app or software you use to plot those Argand diagrams?
Geogebra
Thanks
You are welcome
Sir,do the points in 2 a and 2b need to connect together?
It depends on your teacher.
Sir, can I ask the methodology and results is seperated?
thanks! definitely a great reference
You are welcome.
Sir,how to do methodology??
Tq
Please check with your school teacher for methodology. This page shows the result only.
How to plot the graph in 1B question?
Geogebra
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
Hi ,can I know how to use geogebra
https://wiki.geogebra.org/en/Manual
sorry sir can i know about how to plot question 1 in spiral shape?
You can use geogebra or use paper. It depends on your school teacher
sorry sir can i ask about how to plot question 1 in spiral shape
How to write introduction and methodology?
Please check with your school teacher for methodology and intro. This page shows the result only.
great guidelines for the candidates ! thanks!
You are welcome
sir lee
may i ask how to put methodology in our assignment?
Please check with your school teacher for methodology. This page shows the result only.
Sir, can I ask the methodology and results is seperated?
Yes
Sir,may I know how to write a methodology?
Please check with your school teacher for methodology. This page shows the result only.
how to write methodology?
Please check with your school teacher for methodology. This page shows the result only.
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?
anyway im from penang
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.
thank you very much!!
Sir, can you teach how to do the viva?
Sir graph for ques 1a can be in spiral shape?
Yes
Yes. You can
Sir how to do 1)b) repeat the task?
Redo the power 2, 3, 4, 5
Sir can i know how to connect those points become an exponential spiral?
Using Computer? Or manual?
May i know is the 3c’s argond diagram same as the 3b? *hand drawing
The roots are different
Sir how to plot the graph and draw the diagrams?
You can use geogebra to draw it. Download it and install in your computer or phone
Semester 2 coursework answer when published???
It will be published if they are available
When can i get semester 3 coursework results??
Hi sir, can I know what is the conjugate pair for 3(a) when n=6
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
math is too difficult to me even I do more exercise , how I should do to master every chapter
Please find a good teacher to guide you
When can i get semester 3 coursework results??