vowel changes before nasals

I've heard that some vowel sounds changes a little bit before nasals such as /n/, /N/.
i.e.
/I/ sound in king is generally higher than that of the word "kit", and it's more like /i:/.
Does that mean that the word "king" is pronounced like "keeng"?
What about words like "sin"? is it very much like "seen" or I hear some people pronounce it like "sen".
How are these words pronounced in your accent? I'd like you to tell me where you are from too.

Surrounding consonants can affect a vowel but this effect is resisted where it would cause confusion. Read about it here:

http://www.ling.mq.edu.au/units/ling210-901/phonetics/coarticulation/index.html

Nasal consonants tend to produce nasal vowels. Nasality is not phonemic in English, so speakers tend to nasalize or not nasalize vowels based on convenience (ease of articulation) and habit.

When learning English, you should ignore nasality of vowels unless you are trying to suppress a foreign accent. Even then, recognize that patterns of nasality can vary widely (people in the midwestern U.S. are known for nasalizing just about everything, for example).