- #1

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## Homework Statement

X^2 + 1 = 0

## Homework Equations

find the solution

## The Attempt at a Solution

As simple as this:

what is the solution to x^2 +1 = 0

.... my question, why am I wrong in thinking x^2 = -1 as a possible solution?

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- Thread starter help1please
- Start date

- #1

- 167

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X^2 + 1 = 0

find the solution

As simple as this:

what is the solution to x^2 +1 = 0

.... my question, why am I wrong in thinking x^2 = -1 as a possible solution?

- #2

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- #3

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Oh I see.... Well, a solution to x^2 could be [tex]\pm 1[/tex]. So what is the solution, I am a bit confused. Would it be

x = -1/2

- #4

NascentOxygen

Staff Emeritus

Science Advisor

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Oh I see.... Well, a solution to x^2 could be [tex]\pm 1[/tex]. So what is the solution, I am a bit confused. Would it be

x = -1/2

(-1/2)² = 1/4, so that's not a solution to X² + 1 =0

You are right in re-arranging your equation as X² = -1

now take the square root of both sides.

- #5

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Whether or not a solution exists to this problem depends on what you allow x to be.

- #6

HallsofIvy

Science Advisor

Homework Helper

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No, it's not. You have already said that x^2= -1, not [itex]\pm 1[/itex]. Now you need to get x itself, not x^2. You need to "undo" the square- what's the opposite of squaring?Oh I see.... Well, a solution to x^2 could be [tex]\pm 1[/tex].

You seem to be confused about what "solution to an equation"So what is the solution, I am a bit confused. Would it be

x = -1/2

- #7

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(-1/2)² = 1/4, so that's not a solution to X² + 1 =0

You are right in re-arranging your equation as X² = -1

now take the square root of both sides.

So the solution is

[tex]x = \sqrt{-1}[/tex]

- #8

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So the solution is

[tex]x = \sqrt{-1}[/tex]

Bravo.

- #9

Mentallic

Homework Helper

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So the solution is

[tex]x = \sqrt{-1}[/tex]

[tex]x=\pm\sqrt{-1}[/tex]

- #10

eumyang

Homework Helper

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To the OP: you know the symbol we use for [itex]\sqrt{-1}[/itex], right?[tex]x=\pm\sqrt{-1}[/tex]

- #11

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Yes, it's the imaginary number. :)

- #12

ehild

Homework Helper

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- #13

Mark44

Mentor

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Yes, it's the imaginary number. :)

In other words, what symbol do we use to represent ##\sqrt{-1}##?Which imaginary number?

- #14

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i = sqrt{-1}

- #15

Mark44

Mentor

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Righti = sqrt{-1}

- #16

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For the fundamental theorem of Algebra a polynomial form has always a solution in the set of the complex numebers.

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