section_path: Non-integer powers of complex numbers/Complex exponentiation/Failure of power and logarithm identities
section_name: Failure of power and logarithm identities
paragraph_text: Failure of power and logarithm identities
  
  Some identities for powers and logarithms for positive real numbers will fail for complex numbers, no matter how complex powers and complex logarithms are defined as single-valued functions. For example: