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Do I have to pay a capital gains tax if I rebuy different stocks?
Yes (most likely). If you are exchanging investments for cash, you will have to pay tax on that - disregarding capital losses, capital loss carryovers, AGI thresholds, and other special rules (which there is no indication of in your question). You will have to calculate the gain on Schedule D, and report that as income on your 1040. This is the case whether you buy different or same stocks.