Hello, i need help with this and also please give step by step brief explanations as i need to understand it.

2. (a) Let z=4 -3i and w = 6 - 8/, where i- = -1. Find | z |, arg(z), (3w - 4z), z* (where * indicates the complex conjugate), (zw) and (w/z). Where appropriate, write your answers in the form a + ib, where both a and b are real numbers. Indicate the position of z, w, (3w - 4z), z*, (zw) and (w/z) on an Argand diagram. [8 marks] (b) A Control System has transfer function G(2) = P(=)/Q(=) given by : 3z3 + 4z2 - 49 z + 30 G(z) = 523 - 2z2 + 45z - 18 so that P(z) = 323 + 4z2 - 49 z + 30 and Q(z) = 523 - 2z + 45z - 18. Show = = 3 is a solution of P(:) = 0 and = = 2/5 is a solution of Of:) = 0, . Hence factorise P(:) and Q(=). Hence find all the zeros and poles of G(z). [6 marks] (c) If - n