Finding nth roots of a complex number

[mharten1]

Homework Statement

I have no problem using DeMoivre's Theorem to find nth roots of a complex number. However, I really don't know what this is accomplishing. Usually the book I use explains the concept behind a certain type of problem, but in this case, there is nothing.

I can easily get the correct answer, but I do not know what it means. Any help?

Homework Equations

DeMoivre's Theorem

 

[Slats18]

Well, let us state what the use of these roots are. You can take one of these roots and raise it to the power of n (where n is the number of possible roots) and you will arrive back at the same answer. Also, depending on n, the roots should be positioned equally around the complex plane, with the same angle between each of the roots. This might not explain much, but that's about all I know about the roots =)

 

[Berko]

As well ask why find roots of real numbers? As you go on you will find situations where finding the root of a number is important. Sometimes, it is important knowing where the roots are so as to "avoid them".