Unit 2.5- summer 2018 Flashcards
complex number
have a real and imaginary part
index of radical
is the “root” of the exponent tree aka 1/2 is exponent so index is two
radicand
what is inside brackets
complex number system
contains all real numbers
standard form
a + bi
i^2 can be replaced by
-1
i^0
1
i^1
i
i^2
-1
i^3
-i
i^4
1
i^5
i
factor theorem
when you divide the polynomial by a factor, that is a factor only if f(a –> the root) equals zero
remainder theorem: f(x) is divided by x-n
the remainder is f(n)
remainder theorem: f(x) is divided by ax-b
remainder is f(b/a)
a + bi=c + di
if a =c and b=d
root of -25 can be written as
5i
to find higher powers of i,
divide i^n n by 4 and match the remainder to a power listed above
negative real number has
two square roots in the complex number system
complex solutions can be found for eons that have
no real solutions
every quadratic eon with real coefficients has
solutions in the complex number system
if a + bi is a solution to a polynomial eon,
then a-bi must also be a solution
division statement thingy
quotient times divisor plus remainder = dividend
entire radical
the full, unsimplified radical
before dividing polynomials
check that
1) the exponents are in descending order
2) any missing degrees are inserted with “0”
fundamental theorem of algebra
polynomial with degree n (greater than 1), with real or complex coefficients must have a factor in the form of x-r where r may be real or complex
irreducible over real number
polynomial that has no real roots
teacher thing- exponents
when it is an incomplete exponent, just write it as a fraction ex. g^5/4
radicals multiply…
multiply the stuff under the root!
division don’t mess up
signs while you work!
