In order to rotate a molecule through an angle (theta), a molecular graphics package needs to be able to calculate the new coordinates (x-prime, y-prime) of every point in terms of its previous coordinates (x, y) and the angle (theta).

i. Use the fact that, in the complex plane, multiplication by e^i(theta) produces a rotation through an angle (theta) to derive expressions for x-prime and y-prime in terms of x, y and the angle (theta)

ii. By expressing x and y in terms of polar coordinates, demonstrate that the following identities hold for all angles A and B:

a) sin (A+B) = sinA cosB + cosA sinB

b) cos (A+B) = cosA cosB - sinA sinB