Chapter 5 Complex/Imaginary Numbers 📝

If you get a square root with a negative number

imagine it exists by putting an eye next to it, making the inside of the square root positive, and then solve like normal

What is the most basic unit for an imaginary number

i = square root of -1

Complex Number

combination of real number and an imaginary number

What is the pattern of imaginary numbers that have exponenets

i, -1, -i, 1

Which of the following expressions is written as a complex number?
-5
-1 + i
3i
5
-3i

-1 + i

What is the simplified value of the expression below?
i^10

-1
i
i^3
1
-1

-1

In math, i equals _____.
square root of a negative
negative
negative one
square root of one
squareroot of negative one

square root of negative one

Which of the following is an imaginary number?
-2
√2
∞
2i
2π

2i

When solving a quadratic equation, under what circumstances would the result be two answers that are imaginary numbers?
None of the answers are correct; the results of a quadratic equation will never yield an answer with two imaginary numbers.
When the discriminant is equal to zero
When the discriminant is negative
When the discriminant is positive

When the discriminant is negative

How do you add complex numbers

you just add them (or combine like terms)

Formula for adding complex numbers

(a + c) + (b + d)i

How do you subtract complex numbers

you just minus them (or combine like terms)

Formula for subtracting complex numbers

(a - c) + (b - d)

How do you multiply complex numbers

same as binomials use FOIL method and simplify, (MAKE SURE YOU SIMPLIFY it to the power)

Add and simplify the following expression: (2 - I) + (-5 - 3i)
-3 - 2i
-3 + 4i
3 - 4i
-3 - 4i
-7 - 4i

-3 - 4i

Simplify the following expression:
(3 + 2i) + (1 + i)(1 - i)
3
3 + 2i
5
5 + 2i
3 + 4i

5 + 2i

Multiply and simplify the following expression: (2 + 3i)(4 - 2i)

14 + 8i

Which of the following is a complex number with a non-zero real part and a non-zero imaginary part?
-4
None of the answers are correct.
8 + 4i
8/4
4i

8 + 4i

Subtract and simplify the following expression: ( - 1 + 4i) - (-2 + i)

1 + 3i

How do you divide a complex number?

first change it to a fraction, then multiply it by the denominator's conjugate/denominator's conjugate using foil, if you have two numbers on the top then you split it to wright it in the standard complex form,

Conjugate

a binomial where the sign on the second term has been switched

If you multiply Complex Conjugates you will get a

real number every time

Simplify the following expression
3 + 5i/ 1 + i
2 + 4i
4 - i
-4 - i
4 + i

4 + i

What is the first step in dividing these complex numbers?
1 - 4i/3-4i
Cancel the -4i from the top and the bottom of the fraction.
Multiply the top and bottom of the fraction by 3 + 4i.
Multiply the top and bottom of the fraction by 3 - 4i.
Multiply the top and bottom of the fraction by 1 + 4i.

Multiply the top and bottom of the fraction by 3 + 4i.

Simplify the following expression:
6 + 2i/3-3i

2/3 + 4/3i

What is the complex conjugate of the expression below?
6-2i

6 + 2i

Which two complex conjugates would multiply to equal 13?
(2 + 3i)(2-3i)
(1 + i)(1 - i)
(3 + i)(3 - i)
( 3 + 3i) (3 - 3i)

(2 + 3i)(2-3i)

If your problem has (find the roots of)

it's the same thing as asking for the zeros or the x intercepts, so substitute y for zero

If you get a negative descriminant you

pull the plus or minus and the i/negative outside? seems like you are douple pulling the negative out?????

Find the roots of the equation below: in doc 5,1

x = +/- i

Solve the equation below: in doc 5,2

answer, a

How many roots does the equation below have?
y = -x^2 - 2x + 6
2 complex roots
1 complex root
1 real root
2 real roots

2 real roots

What is the most simplified form of the expression below? in doc 5,3

answer, c

When it comes to solving quadratics with complex solutions, which one of the following statements is FALSE?
If the discriminant is zero, the result will be one real answer.
If the discriminant is negative, the result will be two complex solutions.
If the discriminant is positive, the result will be two real answers.
If the discriminant is zero, the result will be no real answers.

If the discriminant is zero, the result will be no real answers.