FP1 June 2016 Edexcel Exam Paper Question 7

Question7. A complex number z is given by z = a + 2i where a is a non-zero real number. (a) Find z2 + 2z in the form x + iy where x and y are real expressions in terms of a. (4) Given that z2 + 2z is real, (b) find the value of a. (1) Using this value for a, (c) find the values of the modulus and argument of z, giving the argument in radians, and giving your answers to 3 significant figures. (3) (d) Show the points P, Q and R, representing the complex numbers z, z2 and z2 + 2z respectively, on a single Argand diagram with origin O. (3) (e) Describe fully the geometrical relationship between the line segments OP and QR. (2)
It is difficult to write an answer out to a maths question so I will go through the question in detail in the interview.