2017 SQA Advanced Higher Mathematics No. 17 Complex numbers

Find all the roots of a polynomial equation of degree 4, given one of its complex roots. Plot all the roots on an Argand diagram. Instructional exercise consisting of question 17 from the 2017 SQA Advanced Higher Mathematics examination. Where appropriate the alternative methods for solving the problem are also given. Set out in stages of 'try then check' the worked solution to each part of the question. Including indications of where each mark is allocated, and the requirements for that mark, according to the marking scheme.