7. Suppose that f = u + iv is analytic and not identically constant. a) Show that uv is the real part of an analytic function. b) Show that u^2 + v^2 cannot be the real part of any analytic function.
7. Suppose that f = u + iv is analytic and not identically constant. a) Show that uv is the real part of an analytic function. b) Show that u^2 + v^2 cannot be the real part of any analytic function.
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...
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7. Suppose that f = u + iv is analytic and not identically constant.
a) Show that uv is the real part of an analytic function.
b) Show that u^2 + v^2
cannot be the real part of any analytic function.
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