2007 SQA Advanced Higher Maths no.11 Locus of complex numbers

Solve a modulus equation in complex number to find the equation of the locus of the complex numbers. Sketching the locus on an Argand diagram. Instructional exercise consisting of question 11 from the 2007 SQA Advanced Higher Mathematics exam. Set out in stages of 'try then check' the worked solution to each part of the question.