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APARTMENT INVESTMENT & MANAGEMENT CO 10-Q 2010 Exhibit 32.1
Certification of CEO Pursuant to
18 U.S.C. Section 1350, As Adopted Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002 In connection with the Quarterly Report of Apartment Investment and Management Company (the
Company) on Form 10-Q for the quarterly period ended September 30, 2010 as filed with the
Securities and Exchange Commission on the date hereof (the Report), I, Terry Considine, as Chief
Executive Officer of the Company hereby certify, pursuant to 18 U.S.C. § 1350, as adopted pursuant
to § 906 of the Sarbanes-Oxley Act of 2002, to the best of my knowledge, that:
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