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

well sqrt(-4) is just 2i, this process involves taking the negative out so for example sqrt(-225) is just 15i and you leave your answer as that

for your 2nd problem 6x^2-48x+192=0 take it step by step you can either do qud form

(x= (plus or min) (-b*sqrt(b^2-4ac))/2a or you can make it a perfect squared.

6x^2-48x= -192 sub 192 from both sides

x^2-8x= -32 divide by 6

x^2-8x+16= -16 divide 8 by 2 then square the 4 you get then add to both sides

(x-4)(x-4)=-16

(x-4)^2= -16

x-4= 4i

x=4i+4

x= 4i-4 this is because when u take the sqroot of somthing u plus or minus it

HOPE THIS HELPS im only a jr in hs In Calc 2 so PM if u need help with other things

well sqrt(-4) is just 2i, this process involves taking the negative out so for example sqrt(-225) is just 15i and you leave your answer as that

for your 2nd problem 6x^2-48x+192=0 take it step by step you can either do qud form

(x= (plus or min) (-b*sqrt(b^2-4ac))/2a or you can make it a perfect squared.

6x^2-48x= -192 sub 192 from both sides

x^2-8x= -32 divide by 6

x^2-8x+16= -16 divide 8 by 2 then square the 4 you get then add to both sides

(x-4)(x-4)=-16

(x-4)^2= -16

x-4= 4i

x=4i+4

x= 4i-4 this is because when u take the sqroot of somthing u plus or minus it

HOPE THIS HELPS im only a jr in hs In Calc 2 so PM if u need help with other things