Few things i need help with before my Alg II honors final. i need a decent grade on this thing. thanks

Lol so first thing......Solving Complex expressions and quadratic equations and wiritng them in the form a+bi???
-i know what i is, but i dont understand everything about how to solve stuff with it, and what the standard form a+bi means

Ex: sqrt(-4) * sqrt (-4)

Ex: 6x^2-48x+192=0

and then...the functions where there are 2 of them at once bracketed by a { ??? if you go to graph them, do u just graph them both seperately? and are these the same as piecewise defined functions?

No examples of this that i can find

theres something about functions thats in the form f(a+h) - f(a), all of that over h?......how do u solve these?

then finally, could someone walk me thru doing long division with expressions? i understand synthetic division, but the long stuff loses me

Ex: 6x^3 + 6x^2 +12x/
3x^2+4

??? lol you dont have to answer everything, any help is appreciated

thanks