Q4 (a) Simplify each of the following complex numbers, expressing your

answers in Cartesian form:

(i) (7-i)(2+3i)

(ii) i / 2+i

(b) Using de Moivre's Theorem, and without using a calculator, show that

(1 - i)^1066 = -(2^k)i,

where k is a positive integer to be stated.

(c) Find the cube roots of 4i, expressing your answers in the form

z = 2^p e^qi,

where p and q are rational numbers to be stated, with -1