UCLAN FIRE www.uclan.ac.uk/fire University of Central Lancashire School of Engineering FV2301 Assignment Brief (25th October 2017) Assignment Details ANSWER ALL QUESTIONS. PLEASE REMEMBER TO COMPLETE A FRONT COVER SHEET. 1. Calculate and simplify leaving your answers as + : (i) ( 4 + 2j ) - ( 3 - 5j ) [2 marks] (ii) ( 1 + 2j )( 3 + 2j ) [3 marks] (iii) 2. 1 [4 marks] 3+2 Express the complex number 5 + 12j in polar form. Hence find (in polar form) all solutions to the equation z 3 5 12 j 0 and draw them on a diagram of the complex plane. [9 marks] 3. a) Find the real numbers a , b for which b) If z1 3 4 j and z 2 1 3 j , and find z in a bj form, exactly. a j 1 bj 2 j [5 marks] 1 1 1 , z z1 z 2 [7 marks] UCLAN FIRE www.uclan.ac.uk/fire ( 204 + 4. Find 5. By writing 4 3 6. 3 - ) +4 (+1)(2) +4 (+1)(2) Show that, for 0, [4 marks] in partial fractions, find the value of 1 [8 marks] ln = +1 + 1 (+1)2 [8 marks] Remember: You must answer the questions set You must demonstrate that you have met the learning outcomes Presentation Instructions It is your responsibility to ensure that your work is neatly and accurately presented. The work must be: Word-processed Single sided 1.5 or double line spaced Ariel 12 point font Justified Page numbered On A4 paper Margins left and right 3cm Attached to a cover sheet. Marks may be deducted for failure to follow these instructions. Please look at the Student Guide to Assessment for more information. Plagiarism UCLAN FIRE www.uclan.ac.uk/fire The use of work produced for another purpose by you, working alone or with others, must be acknowledged. Copying from the works of another person (including Internet sources) constitutes plagiarism, which is an offence within the University's regulations. Brief quotations from the published or unpublished works of another person, suitably attributed, are acceptable. You must always use your own words except when using properly referenced quotations. You are advised when taking notes from books or other sources to make notes in your own words, in a selective and critical way. Submission Your work must be submitted with: a front cover sheet (detailing the module code and title, coursework title, module name and student name, word count, date submitted). a fully completed School Assessment Cover Sheet. The assignment should be submitted into the year two posting box (Foster Hub) before 12.00pm on the given submission date. The deadline for submission is Monday 8th January 2018 Every attempt will be made to ensure that the work will be marked and available for collection by 29th January 2018 The assignment is worth 40% of the total module assessment. Learning outcomes This assessment will test your ability to meet the learning outcomes as described in your module booklet, specifically: 1. Convert between Cartesian and Polar forms of a complex number and use complex numbers to find the roots of equations 2. Integrate standard functions and find the area under the curve