# TEE102/03 Engineering Mathematics II

TEE102/03 Engineering Mathematics II May 2022

Academic Session 2022

May 2022 Semester

Assignment 1

TEE102/03 Engineering Mathematics II

Evidence of plagiarism or collusion will be taken seriously and the University

regulations will be applied fully. You are advised to be familiar with the University’s

definitions of plagiarism and collusion.

Instructions:

1. This is an individual assignment. Students are required to attach the Assignment

Declaration Form as the front cover of their assignments. Any plagiarism or

collusion may result in disciplinary action to all parties involved.

2. Submit your assignment to the Online Assignment Submission (OAS) system.

Submission of assignments in hard copy will not be accepted.

3. The total marks for Assignment 1 is 100% and contributes 25% towards the

total grade. Marks will be awarded for correct working steps and answer.

4. Assignment 1 covers topics from Unit 1 and Unit 2.

5. Your assignment must be word processed in Time New Roman or Cambria

Math 12pt font. Any additional appendices or attachments must be placed at the

end of the submitted document. Handwritten assignments and photo snap

shot will not be accepted.

6. Assignment Due Date: 12th June 2022.

TEE102/03 Engineering Mathematics II May 2022

Question 1 (30 marks)

(a) Consider that = −3 + 4 ,

(i) find the value of |z|.

[4 marks]

(ii) find the argument of in radians to 2 decimal places.

[4 marks]

Consider that =

−14+2

,

(iii) use algebra to find . Express your answers in + , where and

are real.

[6 marks]

(iv) The complex numbers and are represented by points A and B on an

Argand diagram. Show the points of A and B on an Argand diagram.

[4 marks]

(b) Given

1

π π 4 cos sin

4 4

z i

= +

and

= +

3

2

sin

3

2

2 cos 2

z i ,

(i) find

1 2 zz .

[6 marks]

(ii) find

1

2

z

z

.

[6 marks]

TEE102/03 Engineering Mathematics II May 2022

Question 2 (30 marks)

(a) (i) Use DeMoivre’s Theorem to compute the 5th power of the complex

number = 2 (cos 24 ° + i sin 24°).

[6 marks]

(ii) Express the answer (a)(i) in the rectangular form a + bi.

[4 marks]

(b) (i) Find the 4th roots of 4 + 4i.

[8 marks]

(ii) Show the roots obtained in (b)(i) on an Argand Diagram.

[4 marks]

(c) The point P represents the complex number z on an Argand diagram, where

z – i = 2.

The locus of P as z varies is the curve C.

(i) Find a cartesian equation of C.

[4 marks]

(ii) Sketch the curve C.

[4 marks]

TEE102/03 Engineering Mathematics II May 2022

Question 3 (40 marks)

(a) Evaluate the Laplace transform of the following functions:

(i)

( )

5

cos 4 t

f t e t = +

[6 marks]

(ii)

( ) ( )

6 4 1

t

f t t e = +

[6 marks]

(iii)

( )

5 3

3

15 24

t t f t t = − +

[6 marks]

(b) (i) Find the inverse Laplace transform of

( )

2 2

2

2 3

s

s

−

− +

.

[6 marks]

(ii) Express

2

11 3

2 3

s

s s

−

+ −

in partial fraction form and then find the inverse

Laplace transform of

2

11 3

2 3

s

s s

−

+ −

using the partial fraction obtained.

[10 marks]

(c) Let

( )

4 2 f t t t t = − + − 9 7 12 4

. Find

2

2

d f

dt

L .

[6 marks]

END OF ASSIGNMENT 1