Complex Numbers: 4x^2 + 1 = 0

John Whitaker

Junior Member
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May 9, 2006
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My instructor likes to create problems for which there are no examples or similar problems in our text we might refer to for clarity. So I need to learn how to deal with:

4x^2 + 1 = 0
4x^2 = -1 I think it's possible using " i ", but I don't know the procedure.
Thank you.
John Whitaker
 
Re: Complex Numbers

John Whitaker said:
...I need to learn how to deal with:

4x^2 + 1 = 0
4x^2 = -1 I think it's possible using " i ", but I don't know the procedure.

You have not told us what do you want accomplish with this eqaution - factorize? solve for x? what?

By the way, what is the name of your book?
 
Re: Complex Numbers

Only instruction is to "Solve these equations>"

"Hornsby, Lial, & McGinnis" 8th Ed.
 
To learn how to solve quadratic equations, try here.

Note that quadratics which you cannot solve in the real numbers can still be solved using the Quadratic Formula, which will provide you with the complex-valued solutions.

To learn how to simplify radicals with negatives inside them, try here.

:D
 
Re: Complex Numbers

John Whitaker said:
Only instruction is to "Solve these equations --- you did not tell us that before>"

"Hornsby, Lial, & McGinnis" 8th Ed. --- These are the name of the authors - what is the name of the book? -these authors have written several books at several levels

I'll do a similar problem for you:

ax[sup:2kqix51t]2[/sup:2kqix51t] + 1 = 0

ax[sup:2kqix51t]2[/sup:2kqix51t] - i[sup:2kqix51t]2[/sup:2kqix51t] = 0

(?a * x + i)(?a * x - 1) = 0

Now continue...

By the way - what level of math is this - high school (grade?) - college?
 
I''m sorry... I can do many problems in complex numbers, but I have not seen one structured like this one. I learn not by reading complicatiions, but by following similar examples step by step.

The answer is: {-i/2, i/2}

I need to see how I get there step by step. Thank you.

Intermediate Algebra Lial, etc.
 
John Whitaker said:
I learn not by reading complicatiions, but by following similar examples step by step.
I'm sorry to hear that none of the worked examples in the "Quadratic Formula" lessons and "simplifying with radicals" lessons you studied (from the links provided earlier) was sufficient to your needs. Please try these examples instead:

. . . . .\(\displaystyle 9x^2\, +\, 4\, =\, 0\)

Using the Quadratic Formula:

. . . . .\(\displaystyle x\, =\, \frac{-(0)\, \pm\, \sqrt{(0)^2\, -\, 4(9)(4)}}{2(9)}\, =\, \frac{\pm\sqrt{-144}}{18}\)

. . . . . . . .\(\displaystyle =\, \frac{\pm 12i}{18}\, =\, \pm\frac{2}{3}i\)

Using radicals:

. . . . .\(\displaystyle 9x^2\, =\, -4\)

. . . . .\(\displaystyle x^2\, =\, -\frac{4}{9}\)

. . . . .\(\displaystyle x\, =\, \pm\sqrt{-\frac{4}{9}}\, =\, \pm\frac{2}{3}i\)

:D
 
Re: Complex Numbers

These problems can be done in many "apparantly different" ways. Staple has shown you two ways - here is the third (solution by factorizing)....

ax[sup:rv9hf3zd]2[/sup:rv9hf3zd] + 1 = 0

ax[sup:rv9hf3zd]2[/sup:rv9hf3zd] - i[sup:rv9hf3zd]2[/sup:rv9hf3zd] = 0

(?a * x + i)(?a * x - 1) = 0

Then, either

?a * x + i = 0

x = - i/?a

or

?a * x - i = 0

x = i/?a

So

x = {-i/?a , i/?a}

You choose the method you want to follow.
 
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