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Im having troubles in proving the following result: Let $C^{\bullet}$ be a complex of $R$-modules ($R$ noetherian ring) with non-zero modules in positive degree, and let $M$ be an $R$-module. Assume that $H^i(C^{\bullet})=0$ for $i. Then $H^n( Hom_R(M,C^{\bullet}))=Hom_R(M,H^n(C^{\bullet}))$ Any hint on how to do it?

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