It follows that z = xtiy = re" where x = rcos 0, y = r sin 0, that is, r, 0 are the polar coordinates of z (r = |z), tan 0 = b/a). This gives a Cartesian representation of z = x + iy, and an exponential representation z = reid 4. Use Euler's formula to show that el + e-ie (a) cos ! = 2 el - -10 (b) sin 0 = 2i(c) If z = ref then |z| = r (d) If z = re then 7 = r-id (e) Je"= 1 (f) eanmi = 1, for any integer n (g) ett = -1