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# Algebra Equation

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Hello I am having some trouble with solving the following equation:

\(x^4 = -4\)

I have simplified the equation to \((x^2+2i)(x^2-2i) = 0\)

However, I am having trouble with further solving the equation. I have set the first expression equal to 0, and tried using the quadratic formula and it becomes very messy. Can someone please help me?

Many thanks in advance for any help

Aug 3, 2020
edited by Guest  Aug 3, 2020

#1
+1038
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You could do that, it definately works. If following your way, we would use the difference of squares. But, that would be long and messy.

Instead, we can say that x^2=y, and swap y^2 for x^4.

We get y^2=-4.

So, y is -2i and 2i.

Now, we see that x^2 is -2i and 2i. After solving, the final answers are: x=1+i, x=-1-i, x=-1+i, x=1-i

:)

Aug 3, 2020
#3
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Thank you for your answer. How did you get from x^2 = 2i,-2i to the final answers?

Guest Aug 4, 2020
#2
+169
+1

plug it into symbolab lol

So to do this, try setting a variable \(u=x^2\) to make it simpler. You have \(u^2=-4\) and I think you can do it.

(not trying to be cphil at all)

Aug 4, 2020