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a) Convert the polar equation, r2(cos 0 sin 0 + 1) = 2 into Rectangular form. (3 marks) b) A curve is defined parametrically by x = 3 cos 0 + 2 and y = 2 sin 0. (i) By eliminating the parameter 0, show that the equation represents an ellipse. (5 marks) (ii) Find the center, foci and vertices of the ellipse. (6 marks) c) Given that the forces Fi = 2i + 3j, F2 = -4i +2j and F3 = 6i -12j are acting on a point P, find (i) the resultant force and its magnitude, (3 marks) (ii) the additional force required in order for the forces to be in equilibrium. (2 marks) d) Express the complex number z = v5(1 -i) in trigonometric form. (3 marks) Hence, use the De Moivre's Theorem to find the values of the following. Express your answer in the form of a + bi, where a, b are real number. (i) 23 (2 marks) (ii) (4 marks)