Let z = -5sqrt3/2 + 5/2i and w = 1 + sqrt3i.

Question

(a)  Convert z and w to polar form.

(b)  Calculate zw.

(c)  Calculate z/w.

Answer 1

(a) z = 5(-√3/2 + 1/2i) = 5(cos5π/6 + isin5π/6); w = 2(1/2 + √3/2i) = 2(cosπ/3 + isinπ/3)

(b) zw = 10(cos7π/6 + isin7π/6) = - 5(√3 + i)

(c)z/w = 2.5(cosπ/2 + isinπ/2) = 2.5i