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can a single valued analytic branch of logz be defined on the following sets?
a) {z:1< absolute value of z<2}
b) {Rez>0}
c) {z|Rez>Imz}
can you compute 3^i or solve e^i or log(1+i)? I'm not sure how to go about finding these values?
1 Answer
- Tabula RasaLv 61 decade agoFavorite Answer
To get a single branch the argument needs to be from the interval (0, 2��] or
(-π, π] or (a, a+2π] for any real number a.
a) No. 1< |z| < 2 is a ring and arguments of complex numbers are from the interval
[0, 2π] so when Argz = 0 is one branch and Argz = 2π another.
http://www.core.org.cn/OcwWeb/Mathematics/18-04Com...
b) Yes, it is right half plane, Argz from (- π/2; π/2)
c) Yes, it is a domain under the line y = x, Arg z from (-π/4; π/4)
