# 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.

1

(a) Let z =1+i. Find z^n, where n = 2, 3, 4, β¦, 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, β¦, 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.

#### KK LEE

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Nice work! Thank you!

You are welcome

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 π

I’ll search for this website again for the next coming sem math t assignment π

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

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