I asked this question before and got a wrong answer. Please provide answer in detailed steps and present solution in argand diagram. I will upvote and provide good reviews if answer abide by requirements set out in red fonts:

Question 2: [50 marks] Find and plot the Cartesian equations of the loci of z given by the following equations (for a circle indicate explicitly coordinates of its centre and radius; for an ellipse indicate explicitly coordinates of its foci and semi-axes; for a straight line indicate explicitly its gradient and y- intercept, for a ray indicate explicitly coordinates of its origin and gradient). Present your results in the explicit forms (don't use a calculator). Hint: Replace trig functions by their exact values where appropriate. a ) z+9j = sin - [20 marks] -3j +47 Rubric: 4 marks if the moduli of complex numbers are found correctly; 10 marks if equation of the figure was derived in the correct explicit form; 2 marks if the characteristic coordinates of the figure were found correctly; 4 marks if the figure was correctly presented in the Argand diagram. b) arg (z-2+ 3j) =~ [30 marks] Rubric: 5 marks if the given equation correctly simplified; 10 marks if the equation of the figure was derived correctly; 10 marks if the figure was shown correctly in the Argand diagram