To determine which complex has an inverse-spinel structure, let's first understand what an inverse-spinel structure entails.

In a spinel structure, the general formula is AB_2O_4. In the standard spinel arrangement, A^{2+} cations occupy one-eighth of the tetrahedral sites, while B^{3+} cations occupy half of the octahedral sites in a close-packed oxygen lattice.

In an inverse-spinel structure, half of the B^{3+} ions occupy the tetrahedral sites, and the remaining B^{3+} ions, along with the A^{2+} ions, occupy the octahedral sites.

Let's evaluate the given options:

• Co_3O_4: This compound has a normal spinel structure where Co^{2+} is in tetrahedral sites.
• Fe_3O_4: In this structure, half of the Fe^{3+} ions occupy tetrahedral sites, and the Fe^{2+} and remaining Fe^{3+} occupy octahedral sites, which fits the inverse-spinel format.
• MgAlO_4: This is also a normal spinel.
• Mn_3O_4: Possesses a normal spinel structure.

Based on this analysis, the correct answer is:

Fe_3O_4 is the complex with an inverse-spinel structure.