a) Let a, b E R, not both zero. Find real numbers c, d such that (a+ bi) = c + di. b) Find all cube roots of 1 in C. Give their real and imaginary parts explicitly. These are called the "third roots of unity". c) Complex conjugation is the map C - C sending z = a + bi to z = a - bi, where a and b are the real and imaginary parts of z, respectively. Under what circumstances does complex conjugation define a self- map on the set of n' roots of unity? d) The norm of a complex number z, denoted by | z|, is defined to be the non-negative real number Iz| = (zz) /2. Show that | z1 - Z2| is the usual Euclidean distance between the complex numbers z1, Z2, when these are viewed as points in R2