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During the show, the host asked Cook for his opinion on two new films focusing on Steve Jobs, neither of which are "that flattering," according to Colbert.
While he didn't mention them by name, Colbert was likely referring to "The Man in the Machine," a documentary released earlier this month, and an upcoming biopic directed by Danny Boyle called "Steve Jobs," which stars Michael Fassbender as the Apple CEO.
"I haven't seen them," Cook replied. Describing the films as "opportunistic," Cook went on to defend Jobs.
"The Steve I knew was an amazing human being. He's someone that you wanted to do your best work for. He invented things that other people could not. He saw things other people could not. He had this uncanny ability to see around the corner and describe the future. Not an evolutionary future but a revolutionary future. He was a joy to work with. I loved him dearly and miss him every day."
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Steve Wozniak, who cofounded Apple with Jobs back in 1976, has already watched a rough cut of Danny Boyle's upcoming Jobs biopic. He said that it was a far more accurate portrayal of his friend's life than a previous film, "Jobs," which starred Ashton Kutcher.
Much of the interview focused on the new iPhone 6s and its two big selling points: a new form of input called "3D Touch" and a GIF-like function called "Live Photos." But Colbert also asked Cook about the CEO's letter in October 2014 where he announced that he's a gay man.
"Was coming out an upgrade, or a feature that hadn't been turned on?" Colbert jokingly asked.
"It's like discovering something on your iPhone that it's always done, but you didn't quite know it," Cook replied.
After a bout of laughter, the Apple CEO added that he felt it was time to use his position as a means to help others who might not feel emboldened to be open about who they are. "Life's most persistent question is, 'What are you doing for others?'" Cook said. "I feel a tremendous responsibility to do it."