Show that a branch (Sec. 33) log ::: = In r + iO ( r > 0. a < 0 < u + 27 ) of the logarithmic function can be written log:= - ln(r + y-) + i tan- :_ I , , 1 ( r) 2 x in rectangularcoordinates. Then. using the theorem in Sec. 23. show that the given branch is analytic in its domain of delinition and that there. cl 1 -log:::= - cl::: - :::

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