A 11 and 1/4

Use complete sentences to describe why √-1 ≠ -√1

tekilochka [14]

Well let's say that to compare these two numbers, we have to start with the definition first.

Definition

$\displaystyle \large{ {y}^{2} = x} \\ \displaystyle \large{ y = \pm \sqrt{x} }$

Looks like we can use any x-values right? Nope.

The value of x only applies to any positive real numbers for one reason.

As we know, any numbers time itself will result in positive. No matter the negative or positive.

Definition II

$\displaystyle \large{ {a}^{2} = a \times a = |b| }$

Where b is the result from a×a. Let's see an example.

Examples

$\displaystyle \large{ {2}^{2} = 2 \times 2 = 4} \\ \displaystyle \large{ {( - 2)}^{2} = ( - 2) \times ( - 2) = | - 4| = 4}$

So basically, their counterpart or opposite still gives same value.

Then you may have a question, where does √-1 come from?

It comes from this equation:

$\displaystyle \large{ {y}^{2} = - 1}$

When we solve the quadratic equation in this like form, we square both sides to get rid of the square.

$\displaystyle \large{ \sqrt{ {y}^{2} } = \sqrt{ - 1} }$

Then where does plus-minus come from? It comes from one of Absolute Value propety.

Absolute Value Property I

$\displaystyle \large{ \sqrt{ {x}^{2} } = |x| }$

Solving absolute value always gives the plus-minus. Therefore...

$\displaystyle \large{ y = \pm \sqrt{ - 1} }$

Then we have the square root of -1 in negative and positive. But something is not right.

As I said, any numbers time itself of numbers squared will only result in positive. So how does the equation of y^2 = -1 make sense? Simple, it doesn't.

Because why would any numbers squared result in negative? Therefore, √-1 does not exist in a real number system.

Then we have another number which is -√1. This one is simple.

It is one of the solution from the equation y^2 = 1.

$\displaystyle \large{ {y}^{2} = 1} \\ \displaystyle \large{ \sqrt{ {y}^{2} } = \sqrt{1} } \\ \displaystyle \large{ y = \pm \sqrt{1} }$

We ignore the +√1 but focus on -√1 instead. Of course, we know that numbers squared itself will result in positive. Since 1 is positive then we can say that these solutions exist in real number.

Conclusion

So what is the different? The different between two numbers is that √-1 does not exist in a real number system since any squared numbers only result in positive while -√1 is one of the solution from y^2 = 1 and exists in a real number system.

5 0

2 years ago

Read 2 more answers

Jezebel took a train to visit her uncle. The train traveled at a constant speed of 40 miles per hour. Complete the table. Then,

sergiy2304 [10]

Answer:

[see below]

Step-by-step explanation:

We can tell that for every hour passed the distance traveled by the train would increase by 40 miles.

We can use the equation d = 40t to determine the values of the table. The 'd' is total distance and 't' is the number of given hours.

Two hours:

d = 40(2)

d = 80

Three Hours:

d = 40(3)

d = 120

Four Hours:

d = 40(4)

d = 160

Hope this helps.

4 0

2 years ago

Read 2 more answers

What is the solution for x in the equation?

erastovalidia [21]

The solution for x is D=-4

7 0

3 years ago

?4x y=10 rewrite in slope intercept form

aleksandrvk [35]

Wait, do you mean that y=10 is what you want in slope intercept form? Oh btw I'm not answering this just for the points. I'll actually answer the question

6 0

3 years ago

47/8 as a mixed number

tresset_1 [31]

47/8 is an improper fraction so we need to divide 47 by 8 to get an mixed number.
8 go into 47, 5 times because 5*8 equals 40.
47-40 is 7 that is the left over.
5 7/8 is your mixed number.

6 0

3 years ago