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

Guest Aug 3, 2020

edited by
Guest
Aug 3, 2020

#1**+4 **

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

:)

ilorty Aug 3, 2020

#2**+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)

Inspirational Aug 4, 2020