PreCalc Chapter 2 Test Flashcards Preview

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Flashcards in PreCalc Chapter 2 Test Deck (72)
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0

A _________ number has the form a+bi, where a does not equal 0 and b=0

real

1

A(n) ______ number has the form a+bi, where a does not equal 0 and b does not equal 0

imaginary

2

A _____ _______ number has the form a+bi, where a=0 and b does not equal 0

pure imaginary

3

The imaginary unit i is defined as i=_________, where i^2=___________

square root -1, -1

4

When a is a positive real number, the _____ _____ root of -a ois defined as square root -a=square root ai

principal square

5

The numbers a + bi and a-bi are called _________ ________ and their product is a real number a^2 + b^2

complex conjugates

6

what is the complex conjugate of root 6

root 6

7

what is the conjugate of i

-i

8

how would you do
(2/1+i)-(3/1-i)

do (2[1-i])-(3[1+i])
_______________
(1+i)(1-i)

9

when writing an imaginary quotient in standard form, what cannot be in the denominator

i, rationalize it

10

how would you do
i^44+i^150-i^74-i^109+i^61

divide each power by 4, is remainder is 1, result is i, if the remainder is 2, result is -1, if remainder is 3, result is -i, if remainder is 0, result is 1

11

x^2+1 has ____ real solutions

no

12

what is the pattern for imaginary numbers starting with i^1 and ending with I^4, before repeating itself over and over....

i (or, root -1), -1, -i, 1

13

what is standard form for complex numbers

a+bi

14

every complex number has a ______ number (a) and an _____ number (b)

real, imaginary

15

a+bi
if a=0, what number do you have?

pure imaginary

16

what is the complex conjugate of (3+2i)

(3-2i)
*same exact term with a sign change in the middle*
*things will cancel*

17

how do you rationalize 3+2i/6-i

multiply top and bottom by 6+i

18

when writing complex numbers in standard form, what do you ALWAYS do first

convert to imaginary
ex) root -3 times root -12
=root 3i times root 12i
=-6

19

what 3 solutions do you test first with synthetic division

-1,1,2

20

what does upper bound mean

when you plug in a number into synthetic division and you get all positive numbers as a result, that will be your highest root

21

imaginary roots come in _______, meaning a cubic function will have 2 roots with possible combinations ____.......

pairs,
3 real, 0 imaginary
1 real, 2 imaginary
NEVER 2 real, 1 imaginary

22

True or False, i is a variable

False- it is not a variable, but treat it like it is when performing operations

23

a set of ordered pairs

relation

24

The graphs of all polynomial functions are _______, which means that the graphs have no breaks, holes, or gaps

continuous

25

The ________ __________ _____ is used to determine the left-hand and right-hand behavior of the graph of a polynomial function

leading coefficient test

26

A polynomial function of degree n has at most ___real zeroes and at most _____ turning points

n, n-1

27

When x=a is a zero of a polynomial function f, the following three statements are true:
a) x=a is a ______ of the polynomial equation f(x)=0
b) _____ is a factor of the polynomial f(x)
c) (a,0) is an _____ of the graph of f

zero, (x-a), x-intercept

28

When a real zero of a polynomial function is of even multiplicity, the graph of f _________ the x-axis at x=a, and when it is of odd multiplicity, the graph of f ______ the x-axis at x=a

bounces (touches) crosses

29

A factor (x-a)^k, k>1, yields a _______ _________ x=a of ______ k

repeated zero, multiplicity