section_path: Non-integer powers of complex numbers
section_name: Non-integer powers of complex numbers
paragraph_text: Non-integer powers of complex numbers
  
  In the preceding sections, exponentiation with non-integer exponents has been defined for positive real bases only. For other bases, difficulties appear already with the apparently simple case of n th roots, that is, of exponents 1 / n, {\displaystyle 1/n,} where n is a positive integer. Although the general theory of exponentiation with non-integer exponents applies to n th roots, this case deserves to be considered first, since it does not need to use complex logarithms, and is therefore easier to understand.