Question 1: [50 marks] Find and plot the Cartesian equations of the loci of = 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. z+9j [20 marks] -31 +42 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 connectly presented in the Argand diagram