Answer:
D. 15(cos(23π/12) +i·sin(23π/12))
Explanation:
You want the product 5(cos(π/4 +i·sin(π/4))×3(cos(5π/3) +i·sin(5π/3)).
Complex product
The product is ...
A·cis(a) × B·cis(b) = AB·cis(a+b)
where "cis(x)" means (cos(x) +i·sin(x))
Application
5·cis(π/4) × 3·cis(5π/3) = (5·3)·cis(π(1/4+5/3)) = 15·cis(23π/12)
The product is 15·(cos(23π/12) +i·sin(23π/12)).