Question

Find the cube roots of -8+0i

Answer 1

Is -2 one of the answers

Answer 2

Well, one of them is quite easy: -2

-2*-2*-2 = -8

Answer 3

But for extra points, Daniel the 7th grader, how many cube roots are there of -8?

Answer 4

(I don't think I could have answered that question when I was in 7th grade!)

Answer 5

I thought the answer would just be -2 because I'm not sure what else to do...but I hope there's not more to it

Answer 6

Oh, there is, my dear, there is :-)

Answer 7

Oh noooooooooooooooooooooooooooooooooo :(

Answer 8

So the root young Daniel found is the -2 on the left. The roots are always symmetrically arranged, so the other two are complex conjugates, and are located at \(a\pm bi\)