math test 1

\imaginaryI= \sqrt{-1}

To find out i divide it’s exponent by 4 if it ends in .5

It is -1

To find out I divide it’s exponent by 4 If it ends in .75

It is -i

Complex number

If a and b are real numbers then a+bi is complex

A is real bi is imaginary

a+bi

Real numbers

Include rational numbers, integers, whole numbers, and natural numbers

Rational numbers

Include integers, whole numbers and natural numbers

Integers

Includes whole numbers and natural numbers

Conjugates

Real part stays the same, imaginary is flipped

Nonreal complex numbers

Includes pure imaginary numbers

Radical

The actual thing \sqrt{\placeholder{}}

Radicand

Part under the radical

Index

Part the radical is power to

Adding radicals

Must have the same index and radicand

Product rule for radicals

n\sqrt{a}\cdot n\sqrt{b}=n\sqrt{ab}

Quadratic equation standard formax^2+bx+c=0

0ax2+bx+

\left(a+b\right)\left(a-b\right)

a^2-b^2

A to the 3rd minus b to the 3rd

\left(a-b\right)\left(a^2+ab+b^2\right)

Square root property

Get something squared by itself then simplify

Zero product property

If a and b are complex numbers, when ab=0 a or b must equal 0

Complete the square

1. Divide all terms by a

2. Move c/a to the right side

3. Complete the square on the left side, add the same value to the right side

4. Square root both sides

5. Find x

The quadratic formula

\frac{-b\pm\sqrt{b^2-4ac}}{2a}

Discriminant is a positive perfect square

2 real rational solutions

Discriminant is positive not perfect square

2 irrational real solutions

Discriminant is 0

1 real solution

Discriminant is negative

2 imaginary solutions

Pythagorean theorem

a^2+b^2=c^2

Distance

Rate(time)

Rate

Distance/time

Time

Distance/speed

Rates of work

1/rate of worker 1 + 1/rate of worker 2 = 1/rate when together