In the metallurgical extraction of copper, following reaction is used:
$$\text{FeO} + \text{SiO}_2 \rightarrow \text{FeSiO}_3$$
FeO and FeSiO$$_3$$ respectively are.

In the metallurgical extraction of copper, the reaction is: $$\text{FeO} + \text{SiO}_2 \rightarrow \text{FeSiO}_3$$.

In metallurgy, gangue refers to the earthy impurities (unwanted material) associated with the ore, flux is a substance added to remove gangue by combining with it, and slag is the fusible product formed when flux reacts with gangue.

In copper extraction, the ore is copper pyrite (CuFeS$$_2$$). During smelting, FeS is converted to FeO, which is the unwanted impurity (gangue) that needs to be removed. SiO$$_2$$ (silica) is added as flux to combine with the gangue (FeO), producing FeSiO$$_3$$ (iron silicate) as the slag, which is easily separable.

Answer: FeO is the gangue and FeSiO$$_3$$ is the slag; hence, the correct answer is Option D.