Let Log(z) denote the principal branch of the complex logarithm, so that Log(z) = In |z| + i Arg(z), z #0, %3D where In r denotes the usual natural logarithm of the number r > 0. Consider now the formula f(2) = Log(z? + i). (i) For which values of z E C does this formula define a function of complex variable? (ii) Find the largest open set A such that f(2) is holomorphic on A and compute f'(z) for z E A.

Let Log(z) denote the principal branch of the complex logarithm, so that Log(z) = In |z| + i Arg(z), z #0, %3D where In r denotes the usual natural logarithm of the number r > 0. Consider now the formula f(2) = Log(z? + i). (i) For which values of z E C does this formula define a function of complex variable? (ii) Find the largest open set A such that f(2) is holomorphic on A and compute f'(z) for z E A.

Name: Could you explain how to show this in detail? Let Log(z) denote the pr
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Description: Could you explain how to show this in detail? Let Log(z) denote the principal branch of the complex logarithm, so thatLog(z) = In |2| + i Arg(z),z #0,where In r denotes the usual natural logarithm of the number r > 0.Consider now the formulaf(2) = Lo

Advanced Engineering Mathematics

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ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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Could you explain how to show this in detail?

Let Log(z) denote the principal branch of the complex logarithm, so that
Log(z) = In |2| + i Arg(z),
z #0,
where In r denotes the usual natural logarithm of the number r > 0.
Consider now the formula
f(2) = Log(2? + i).
(i) For which values of z EC does this formula define a function of complex variable?
(ii) Find the largest open set A such that f(z) is holomorphic on A and compute f'(z) for
Z E A.

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