“As” is used properly followed by a subject, then a verb. “Like is properly preceded by a verb and then followed by a noun/pronoun.
Both are used to make comparisons.
“As I have said many times, I do not want you playing hookey like your brother.”
“You will end up a hoodlum like him.”
“If you follow in her footsteps, you will go as she did.”
The use of “like” where “as” should be is an informalism common in American English:
“Nobody does it like you do.”
“Hopefully, it won’t rain tomorrow, as I plan to go to the beach.” I am unaware of when I picked up the habit of misusing “hopefully” as shorthand for the phrase “I am hopeful,” but I know I am not alone; I am grateful to my daughter’s Spanish teacher for raising my consciousness about it.
A “compliment” [per Webster’s New World Dictionary] is an expression of admiration, or a gift given for services (tip); a complimentary object is given free as a courtesy.
“Complement” is that which completes or brings to perfection. Complementary objects operate together, each providing what the other does not.
Examples of proper usage:
“My compliments to the chef for providing complementary proteins in our vegetarian lunch this afternoon.”
“The owner of the restaurant is a family friend: She sent over a complimentary bottle of wine which complemented our meal quite well.”