4.3-6 Quiz

Question 1

Radical

Answer 1

Any expression with a square root, cube root, etc.

Question 2

Radical Symbol

Answer 2

√

Question 3

First 20 Perfect Squares

Answer 3

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400

Question 4

Simplifying Radicals

Answer 4

Perfect Squares - Take the square root if the number
Non-Perfect Squares - Break the radical down using the largest perfect square, take the sqaure root of the perfect square, and leave the leftover under the radical symbol
Both - If there is a coefficient outside the radical, multiply this with any number you take out

Question 5

Quadratic Equations of The Square Root Form

Answer 5

ax^2+c=0

Question 6

ax^2+c=0 Can Be Solved Using

Answer 6

Square root property

Question 7

Steps to Solving Quadratics By Square Roots

Answer 7

1. Isolate x^2
2. Take the square root of both sides
3. Simplify the radical, and write as list of x

Question 8

Imaginary Numbers

Answer 8

Equations with no real solution defined to represent their solutions

Question 9

Imaginary Unit

Answer 9

i
Defined as i=√-1

Question 10

Pure Imaginary Number

Answer 10

bi
b represents real number
i is the imaginary part

Question 11

Steps to Simplifying Negative Square Roots

Answer 11

1. Rewrite √-a as √-1*a
2. Break a down if it is not a perfect square
3. Simplify the radical, recalling that √-1=i

Question 12

Powers of “i”

Answer 12

Base four number system
i^1=i
i^2=(√-1)^2=-1
i^3=i^2i^1=(-1)(i)=-i
i^4=i^2i^2=(-1)(-1)=1

Question 13

Memorize Powers of “i”

Answer 13

i=√-1
i^2=-1

Question 14

Complex Number

Answer 14

Real number and a pure imaginary number that are not like terms and can not be combined

Question 15

Standard Form of a Complex Number

Answer 15

a+bi
a is real number
i is pure imaginary number

Question 16

Complex Conjugates

Answer 16

Two complex numbers in the form a+bi and a-bi
(a+bi)(a-bi)=a^2+b^2

Question 17

Product of Two Conjugates

Answer 17

Always a real number

Question 18

Conjugates

Answer 18

(a+b)(a-b)

Question 19

Dividing Complex Numbers

Answer 19

Denominator is a monomial - Multiply top and bottom by “i”
Denominator is a binomial - Multiply top and bottom by the conjugate
Careful - “i” can not be in the denominator of a complex number

Question 20

Completing the Square

Answer 20

Taking any quadratic equation, creating a perfect square trinomial, and solving it in a similar way

Question 21

Steps to Completing the Square

Answer 21

1. Rewrite as ax^2+bx=c
2. Divide both sides by “a” so it becomes x^2+bx=c
3. Complete the square by taking half of b, square it, and adding it to both sides of the equation
4. Factor the perfect square trinomial
5. Take the square root of both sides, creating two cases with a negative and positive value
6. Solve both equations, simplifying all irrational and complex answers

Question 22

CTS Form

Answer 22

ax^2+bx=c
(b/2)^2