(a) Show that (3 – i)^2 = 8 – 6i.

(b) The quadratic equation

az^2 + bz + 10i = 0,

where a and b are real, has a root 3 – i.

(i) Show that a = 3 and find the value of b.

(ii) Determine the other root of the equation, giving your answer in the form p + iq.

(Hint for (ii): Use the fact that the sum of the roots in any quadratic is –b/a).