when do I use 'Dear ***' , when do I use 'Hi, ***'

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I presume that you are talking about the greeting of a letter. 'Dear..' is always a right choice. Use 'Hi...' only in very casual letters to friends or co-workers.

Thank you!
I always get confused when I tried to start to email, should I use 'dear ' or 'hi' , does ' dear' mean something that I like the person or 'hi' just purely used in a casual way?

Dear as a form of address has no connection to dear (someone you are fond of).

It is the formal and standard greeting and should certainly be used in all serious or formal writing. To use anything else in a letter, even an informal one, would look rather odd to me.

Hi - this gets used only in informal communication. It's now quite common in emails.

I would like anyone to answer this for me.
One of my student has used this link and mailed me only as Dear without even using madam and ended the mail as regards.
Is this way of communication with the faculty is formal or informal