Burning of a piece of magnesium wire is a synthesis reaction.

Explanation

**Step-by-Step Solution:**

1. **Understanding the Reaction**: The burning of magnesium wire in air is a chemical reaction. When magnesium (Mg) is burned, it reacts with oxygen (O₂) present in the air.

2. **Identifying the Products**: The product formed from this reaction is magnesium oxide (MgO). The chemical equation for this reaction can be written as:
\[ 2 \text{Mg} + \text{O}_2 \rightarrow 2 \text{MgO} \]
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