Q1.

(a) (i) Use de Moivre's theorem to evaluate 15 4 in two decimal places.

(ii) Given that is a complex number, use your answer obtained from part 1(a)(i) to solve 2 5 + (10 + ) = 0. Leave your answer in two decimal places.

(b) Given that is a complex number, sketch the common region shared by the following locus: | 2| < 3 2() + () 6

Q3.

(a) Find the parametric equations for the curve, = 2 + 1 that joins two points from P(0, 1) to Q(1, 2).

(b) Hence, use your answer obtained from part 3(a) to find the work done by the vector field, (, ) = . Leave your answer in two decimal places