1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
DanielleElmas [232]
2 years ago
7

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

Mathematics
2 answers:
tekilochka [14]2 years ago
5 0

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

<u>D</u><u>e</u><u>f</u><u>i</u><u>n</u><u>i</u><u>t</u><u>i</u><u>o</u><u>n</u>

\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.

<u>D</u><u>e</u><u>f</u><u>i</u><u>n</u><u>i</u><u>t</u><u>i</u><u>o</u><u>n</u><u> </u><u>I</u><u>I</u>

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

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

<u>E</u><u>x</u><u>a</u><u>m</u><u>p</u><u>l</u><u>e</u><u>s</u>

\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.

<u>A</u><u>b</u><u>s</u><u>o</u><u>l</u><u>u</u><u>t</u><u>e</u><u> </u><u>V</u><u>a</u><u>l</u><u>u</u><u>e</u><u> </u><u>P</u><u>r</u><u>o</u><u>p</u><u>e</u><u>r</u><u>t</u><u>y</u><u> </u><u>I</u>

\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.

<u>C</u><u>o</u><u>n</u><u>c</u><u>l</u><u>u</u><u>s</u><u>i</u><u>o</u><u>n</u>

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.

ivolga24 [154]2 years ago
4 0

Answer:

Therefore \sqrt{1} \neq -\sqrt{1}

Step-by-step explanation:

\sqrt{-1}  \\ cannot be calculated as no two identical numbers that are multiplid could give -1. However - \sqrt{1} means -1 x \sqrt{1} = -1 x 1 = -1 . Therefore \sqrt{1} \neq -\sqrt{1}

You might be interested in
Please help me!!! brainliest
nevsk [136]

Answer:

1, 2, 4

Step-by-step explanation:

  1. 4 1/12·2 2/3 = 49/12·11/4 = 49/12·33/12 = 1617/144 = 11 11/48 Good
  2. 2 1/5·6 1/4 = 11/5·25/4 = 44/20·125/20 = 5500/400 = 13 3/4 Good
  3. 1 1/2·3 1/5 = 3/2·16/5 = 15/10·32/10 = 480/100 = 4.8 Doesn't Work
  4. 3/4·8 1/5 = 3/4·41/5 = 15/20·164/20 = 2460/400 = 6 3/20 Good
  5. 5 1/2·5 = 11/2·5 = 55/2 = 27 1/2 Doesn't Work

(Note: Division of big numbers should be done by simplification, although not shown here.)

5 0
2 years ago
Read 2 more answers
Efficiency is the ratio of output work to input work, expressed as a percentage. Light bulbs put out less light energy than the
grandymaker [24]

Answer:

  10%

Step-by-step explanation:

Using the given formula with the given data, we have ...

  efficiency = output work / input work

  = (10 J)/(100 J) = 0.10 = 10%

7 0
3 years ago
Use Cramer’s Rule to solve system of equation.
alisha [4.7K]

\left\{\begin{array}{ccc}5x+2y=4\\3x+4y+2z=6\\7x+3y+4z=29\end{array}\right\\\\A=\left[\begin{array}{ccc}5&2&0\\3&4&2\\7&3&4\end{array}\right]\\\\\det A=5\cdot4\cdot4+3\cdot3\cdot0+2\cdot2\cdot7-7\cdot4\cdot0-3\cdot2\cdot5-3\cdot2\cdot4=54\\W_x=\left[\begin{array}{ccc}4&2&0\\6&4&2\\29&3&4\end{array}\right]\\\det W_x=4\cdot4\cdot4+2\cdot2\cdot29+6\cdot3\cdot0-29\cdot4\cdot0-3\cdot2\cdot4-6\cdot2\cdot4=108

W_y=\left[\begin{array}{ccc}5&4&0\\3&6&2\\7&29&4\end{array}\right]\\\det W_y=5\cdot6\cdot4+3\cdot29\cdot0+4\cdot2\cdot7-7\cdot6\cdot0-29\cdot2\cdot5-3\cdot4\cdot4=-162\\W_z=\left[\begin{array}{ccc}5&2&4\\3&4&6\\7&3&29\end{array}\right]\\\det W_z=5\cdot4\cdot29+3\cdot3\cdot4+6\cdot2\cdot7-7\cdot4\cdot4-3\cdot6\cdot5-3\cdot2\cdot29=324\\\\x=\dfrac{\det W_x}{\det A}=\dfrac{108}{54}=2\\\\y=\dfrac{\det W_y}{\det A}=\dfrac{-62}{54}=-3\\\\z=\dfrac{\det W_z}{\det A}=\dfrac{324}{54}=6

5 0
3 years ago
When placed in the box below, what expression will complete an example of the commutative property of addition 7(2+9)= ?
ANEK [815]

The expression for 7(2+9) IS A(B+C) which is distributive property of addition over multiplication.

Only two arithmetic procedures are subject to the commutative property: Multiplication and Addition

 A + B = B + A Which is Commutative property of addition

A.B = B.A, which is a commutative property of multiplication.

Distributive property is A(B+C) =AB+AC

The operation on numbers that are available in brackets can be distributed for each number outside the bracket, according to the distributive property. It is one of the mathematical properties that is used the most. Commutative and associative qualities are the other two important features.

from the given data 7(2+9) =7*2+7*9

                                                =14+63

                                                =77

Now, we can clear that 7(2+9) =7(9+2)

Hence, the expression for commutative property of addition is A(B+C) = AB+AC.

To learn more about commutative property, visit

brainly.com/question/28387735

#SPJ1

6 0
1 year ago
72x2 + 39x + 207 = 0​
JulsSmile [24]
The answer is x=-9



Hope this helped:)
6 0
2 years ago
Other questions:
  • The recipe calls for 4 3/4 cups of flour of flour she has 2 2/3 how much more flour does she need?
    6·2 answers
  • Helppppp me plzzz with this!!
    10·1 answer
  • I will Give( Brainliest) and (50 Points)
    9·2 answers
  • Function k is a linear function with a slope of 1/2 that passes through the point (4,2). What equation represents Function K?
    10·1 answer
  • 30 POINTS!! Help me please!
    8·1 answer
  • Can sb pls solve this?​
    7·1 answer
  • I NEED HELPPPP ON THIS! <br> 3 questions
    14·1 answer
  • Simplify.<br><br> (–28xy) ÷ (–4)<br><br><br> −7xy <br><br> 17ab <br><br> −17ab <br><br> 7xy
    12·1 answer
  • 5
    6·1 answer
  • Find The Surface Area Of The Pyramid
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!