STPM 2018 Term 1 Mathematics (T) Coursework PBS AssignmentSTPM Coursework Sample Solution
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:
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.
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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