unit 3 Flashcards
simplifying radicals
find biggest perfect square, simplify to its entirety
simplyifying radicals with variables
divide exponent on inside by the root index
rationalize the denominator of square root expressions
multiply top and bottom by that sqaure root
- if there is more than 1 term, multiply it by its conjugate (FL for bottom)
adding/subtracting radical expressions
- radicand needs to be the same. simplify each expression to have the same radicand, then combine like terms
multiplying radical expressions
radicands don’t have to be the same, MULTIPLE WAYS based on the expression
1) multiply outside/outside and inside/inside
2) distribute and combine like terms
3) foil, combine like terms, simplify radicals if necessary
4) sqaure and rewrite as a foil problem
solving radical equations
- isolate the radical
- sqaure both sides
- check solutions with original question!!!!!! this is because there may be extraneous solutions
- move everything to one side (quadratic) or get variable alone (solve for x) (linear) and solve
- for cube/4th root do the same except raise to the 3rd/4th power
solving double radical equations
- isolare one of the radicals
- square both sides but foil one side
- isolate remaining radical as much as possible
- sqaure both sides
- check solutions
imaginary numbers
sqaure root of negative 1 = i
- if you simplify a radical with even root index and negative radicand, get rid of i
complex numbers
- imaginary (i) vs real numbers)
- complex # form: a + bi
a
adding/subtracting complex numbers
- combine real exponents with each other and imaginary components with each other
- sum= resultant
- follows a + bi
multiplying complex numbers
- each must be written as a + bi
- foil/multiply as is
dividing complex numbers
- needs to be written in a + bi form
- multiply top and bottom by conjugate of denominator, foil both top and bottom and then combine like terms
- i cannot be in the denominator
factoring the sum of perfect sqaures
- MUST use i form
- (a + bi) (a-bi) = a2 + b2
- ex. x2 - 81
- (x+9i) (x-9i)
powers of i
0 = i0= 1
0.25= i1= i
0.5= i2= -1
0.75= i3= -i
always pattern of (1,i, -1, -j_
i by itself = 0
ex. i4= 1. i5= i, i6= -1, i7= -i
- to simplify power of i, divide by 4 to solve