Unit 8.6 to 8.7 and Complex Numbers

Remember that when dividing by a negative number…

The sign flips directions

for writing the domain if x is greater than a number then the arrow on the graph goes…

Right

For writing the domain If x is less than the number then the arrow on the graph goes…

Left

For radicals like this what do you need to know to solve?

Instead of setting the equation like x+4 greater than or equal to to 0 do

✅ x+4> 0 and solve

For general 8.7 problems how do you solve?

1. Take the square out of the radical

2. Set the equation in the radical to the greater than or equal sizing and zero

3. Simplify the equation : subtract/ add anything —→ divide, multiply

4. Plot the number on the number line, move the arrows

5. Write the domain in interval notation

When doing 8.6-8.7 when should you check your work?

Always!!!

When writing the domain in interval notation the numbers that give you error on the calc. when you check should be

Put in parentheses

8.7 is when you….

Find the domain of the radicals in interval notation

In 8.7 if you see that a radical has an odd index than the domain is…

All Real Numbers:(-\infty,\infty)

In 8.7 you have to know that you can’t have negative number in the radical or equal to a negative number

….However,

Even index, if the index is odd it can be negative or positive

For a problem like this what are the steps to solve?

1. Factor the quadratic fully

2. Set the answers to the factoring to greater than or equal to zero ( the sign faces left)

3. Plot the numbers on the number line

4. Understand that the far left of the number line is positive, the middle with the numbers potted are negative, and the far right is positive

5. Write the domain in interval notation

8.6 Solving rational equations how would you solve a problem like this

1. Simply the equation: subtract, add, divide multiply

2. Depending on the index square, cube etc the equations on both sides

3. Foil and simplify

4. create a quadratic ⭐️ the third term of the quadratic needs to be positive

5. Factor the answers and check! 😀

8.6 How would you solve a problem like this?

1. For problems like this there needs to be the same index or else you can’t solve

2. Sqare ir cube or wtv each side, remove the expression out of the radicals

3. Simplify

4. Check ! 💁🏾

For 8.7 word problems remember that…

⭐️Somewhere in the problem they will give you a number and you have to plug that number into the radical and solve

i equals to

-1

i² equals to

-1

For larger numbers look for the largest multiple of I to break it apart, any multiple of 4 for i is equal to

1

i³ is equal to

-i

i^4 is equal to

1

i^5 is equal to

i

i^6 is equal to

-1

i^7 is equal to

-i

i^8 is equal to

1

a+ or - bi is a

Standard form

In the standard for a+ or - bi a is the

Real part

In the standard equation a+ or - bi, bi is the

Imaginary part of the equation

The ‘a’ in the a + or- bi equation can be

Negative

What is a faster way to solve an equation like this?

1.) square the 8 and make the equation minus to the multiplication of the -2i×2i=-4i²

2.) solve the equations = 64 +4 = 68

3) the final answer is 68

A negative number inside the radical and an even index means

An imaginary number

Greater than symbol for absolute value inequalities means

Or

Less than symbol for absolute value inequalities means

And!!