nth roots of numbers

[tut_einstein]

I'm slightly confused about why complex numbers are required to find all n roots of a number. Is it specifically because of the fact that you can represent complex numbers as a rotation of the plane? I understand why a number should have n roots, I'm just not sure which part of the definition of complex numbers allows this.

Thanks!

 

[mmm4444bot]

I'm not entirely understanding your confusion.

When you write the phrase "a number", are you thinking "a Real number" ?

For now, I'll just make sure that you realize that all Real numbers are also Complex numbers. In other words, the set of Real numbers is a subset of the set of Complex numbers.