Question

Multiply:
5(cos Pi/3 + i sin Pi/3)times 2 (cos Pi/4 + i sin Pi/4) and leave the answer in trigonometric notation.

Answer 1

Using the following result:
(cosα+isinα)(cosβ+isinβ)
=cosαcosβ-sinαsin&beta + i(sinαcosβ+cosαsinβ)
=cos(α+β) + i sin(α+β)

So
5(cos Pi/3 + i sin Pi/3)times 2 (cos Pi/4 + i sin Pi/4)
is simply
5*2 (cos(π/3+π4)+i sin(π/3+π/4))
=10(cos(7π/12)+i sin(7π/12))