Synthetic query generation has become essential for training dense retrievers, yet prior methods generate one query per document, focusing solely on query quality. We are the first to systematically study multi-query synthesis and discover a quality-diversity trade-off: high-quality queries benefit in-domain tasks, while diverse queries benefit out-of-domain (OOD) generalization. Through controlled experiments on 4 benchmark types across Contriever, RetroMAE, and Qwen3-Embedding, we find that diversity benefit strongly correlates with query complexity (r$\geq$0.95, p<0.05), approximated by content words (CW). We formalize this as the Complexity-Diversity Principle (CDP): query complexity determines optimal diversity. Based on CDP, we propose complexity-aware training: multi-query synthesis for high-complexity tasks and CW-weighted training for existing data. Both strategies improve OOD performance on reasoning-intensive benchmarks, with compounded gains when combined.

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