1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Complex exponent

  1. Jun 14, 2012 #1
    This is just a quick question which arose when doing an exercise, where you had to evaluate a complex exponent, az.
    As you know you can easily generalize exponents to complex numbers using the fact that:
    az = eln(a)[itex]\cdot z[/itex]
    However, as you also know the function lnz is multivalued, i.e. ln(rexp(i[itex]\theta)) = ln(r) + i(\theta[/itex]+2k[itex]\pi[/itex]). Does that mean that the result for az should also be multivalued?
  2. jcsd
  3. Jun 14, 2012 #2
    Yes, the value [itex]a^z[/itex] is multivalued. However, if we take the principal branch of the logarithm, then we get only one value. This principal branch is what is often meant with [itex]a^z[/itex].
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook