+0

# What is the solution of the equation over the complex numbers?

0
73
3

What is the solution of the equation over the complex numbers?

x^2+24=0

Guest Oct 9, 2017
Sort:

#1
+339
0

Subtract 24 from both sides.

x ^ 2 = -24

x = 24i

supermanaccz  Oct 9, 2017
#2
0

Guest Oct 9, 2017
#3
+1493
0

By definition, $$\sqrt{x^2}=|x|$$. I know this because if you graph both functions, the output will be the same.

 $$x^2+24=0$$ Subtract 24 from both sides. $$x^2=-24$$ Take the square root from both sides. $$|x|=\sqrt{-24}$$ The absolute value symbol means that the answer is in its positive and negative forms. $$x=\pm\sqrt{-24}$$ Now, let's change the square root to an imaginary form. We can apply the radical rule that $$\sqrt{-a}=\sqrt{-1}\sqrt{a}$$ $$x=\pm\sqrt{24}\sqrt{-1}$$ We know that by definition, $$i=\sqrt{-1}$$ $$x=\pm i\sqrt{24}$$ We can simplify the square root of 2 to its simplest radical form. $$x=\pm2i\sqrt{6}$$
TheXSquaredFactor  Oct 9, 2017

### 34 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details