Complex Analysis: Theory and Applications · Problem 1.4.2

Complex Numbers — Howell & Matthews

Mathematics — Complex Analysis · exponential-notation-products

Problem

Use exponential notation to show that (a)

(\sqrt{3} - i)(1 + i\sqrt{3}) = 2\sqrt{3} + 2i

. (b)

(1+i)^3 = -2 + 2i

. (c)

2i(\sqrt{3}+i)(1+i\sqrt{3}) = -8

. (d)

\dfrac{8}{1+i} = 4 - 4i