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