Quadratic Equations and Complex Numbers

Question 1

Difference of squares

Answer 1

a² - b² = (a+b)(a-b)

Question 2

How to solve a binomial with an exponent that isn’t 1

Answer 2

1. Multiply the x² by the last number without x
2. Find the two numbers that add up to the middle number and multiply to the new last number
3. Keep the old last number in the new equation

Question 3

How to find the zeros in a binomial

Answer 3

Factor the equation and solve each x with zero

Question 4

Complex number

Answer 4

a+bi

Question 5

What is a in a+bi

Answer 5

The real portion

Question 6

What is bi in a+bi

Answer 6

The imaginary portion

Question 7

What is √-1

Answer 7

i

Question 8

What is i²

Answer 8

-1

Question 9

What is the complex conjugate?

In imaginary factorials

Answer 9

(a+bi)(a-bi)

Question 10

How to divide complex numbers

Answer 10

Multiply the top and bottom by the conjugate
(the opposite)
Ex. 3x-2; 3x+2

Question 11

Every _ power of i; the pattern repeats itself

Answer 11

4th

Question 12

What is the pattern of i

Answer 12

1
i
-1
-i

Question 13

Steps to find what i to a power equals

Answer 13

1. Divide the exponent by 4
2. Remainder is the answer to the problem

Question 14

What is a conjugate?

Answer 14

The same numbers but opposite addition/subtraction

Question 15

How to complete the square

Answer 15

1. a must = 1
2. put a and b on the same side and c on the opposite side
3. (b/2)²
4. Factor
5. Solve

Question 16

Quadratic formula

Answer 16

x= -b+/- √(b)² - 4ac

2a

Question 17

Steps to solve with the quadratic formula

Answer 17

1. Identify a, b, c
2. Substitute into the formula
3. Simplify

Question 18

If the discriminant is (+)

Answer 18

There are 2 real solutions

Question 19

If the discriminant is (-)

Answer 19

There are 2 imaginary solutions

Question 20

If the discriminant is (0)

Answer 20

There is 1 real solution

Question 21

The pattern of i remainders

Answer 21

1: 1
1/4: i
1/2: -1
3/4: -i

Question 22

What should the answer look like when asked to solve

Answer 22

Like solving for zeros
Ex. x=# x=-#

Question 23

True or false…
Write +/- on all square root equations

Answer 23

True

Question 24

Solve an equation using square roots

Answer 24

Put (x-#)² = # and take the square root of both sides

Question 25

Read Carefully!
True or false, when using the quadratic formula, you have to put the b value over 2a as well as the 4(a)(c) value

Answer 25

True

Question 26

Discriminant

Answer 26

b²-4ac

Question 27

1:
1/4:
1/2:
3/4:

Answer 27

1
i
-1
-i

Question 28

What happens in an i to the power equation

Answer 28

The i replaces anything that was there before it and is multiplied by the value in front of it

Question 29

When do you complete the square?

Answer 29

When you try to factor and it doesn’t work

Question 30

Rules to complete the square

Answer 30

The x² coefficient HAS to be 1
You have to take the square root of both sides