adjective
BAD : I was curious what she would look like.
GOOD : I was curious to know what she would look like.
BAD : I'm very curious of the country and its inhabitants.
GOOD : I'm very curious about the country and its inhabitants.
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curious about/as to : 'I'm curious as to how he knows our address.'
curious to see/know etc: 'We're all curious to see what his new girlfriend is like.'