imaginary roots with Quadratic formula

Can the number √-1 be simplified?

the number √-1 cannot be simplified

If the equation starts with a term on the left side (ex: 12=-3ײ+16x) then how do you set it equal to zero.

Make the right side transfer to the left since the equal sign should always be on the left. Here you would do +3ײ and -16x

Is there any real number multiplied by itself that would equal negative 1?

no

√-1 is considered ______

imaginary

The letter _ is used to represent √-1

i

the letter i represents what?

√-1, and imaginary number

If a quadratic equation does not cross the ____, the solutions will be _____

x-axis, imaginary

What is the quadratic formula?

The Quadratic Formula “x=(-b±√(b²-4ac))/(2a)” is used to find the values of x from any quadratic equation, usually in the form “ax²+bx+c=0”

What are complex numbers?

Numbers/equations that have an imaginary number

What is the “root” of an equation?

The solution

What does the form a+bi mean?

a and b represent the real numbers. i represents the imaginary number.

i¹ = ?

i

i² = ?

-1

2i + 3i = ?

5i

-1 = ?

i²

i + i = ?

2i

i³ = ?

-i

i⁴ = ?

1

Just like a variable, the symbol i goes ____ the number

behind

Would you add a i when simplifying this?

-√36

No, because the negative symbol is on the outside

Would you add a i when simplifying this?

√-36

Yes, because the negative symbol is on the inside

Simplify √-200

√-100, √2, i

10i√2

Simplify √-98

√49,√2, i

7i√2

How do you simplify a number that doesn’t have a square root (like √-98) ?

If the number cannot be squared, divied by 2 and represent the equation as i√x√2i. Than simplfy √x and represent as xi√2. √-98 would become 7i√2

When combining like terms do you add i or √2 together?

No

Simplify the expression to a+bi form:

√36 - √-4 - √121 + √-64

-5 + 6i

Simplify the expression to a+bi form:

−√36​ + √−128 ​− √36​ + √−200​

-12 + 18i√2

Simplify the expression to a+bi form:

-√16 + √-72 + √121 + √-2

7+ 7i√2

What are the roots of the equation?

6ײ-11x-3=0

11 ± √193 / 12

What are the roots of the equation?

12=−3x²+16x

16 ± √112 / 6

What are the roots of the equation?

20x²−5=21x

x = {5/4, - 1/5)

*Remember your parenthesis on everything

Fully simplify.

(−2√−49​)(5√−100​)

700