Question

construct the analytical whose real part is cos x. cosh y
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Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Construct the analytical whose real part is cos x. cosh y:

Explanation:

• By using the usual notation for the Cauchy Riemann equations,
• u = sin(x)cosh(y) so ∂u/∂x = cos(x)cosh(y) and ∂u/∂y = sin(x)sinh(y)
• Then the Cauchy Riemann equations tell us that ∂v/∂y = ∂u/∂x = cos(x)cosh(y) and ∂v/∂x = -∂u/∂y = -sin(x)sinh(y)
• Integrating ∂v/∂y = cos(x)cosh(y) gives v = cos(x)sinh(y) + f(x)
• Integrating ∂v/∂x = -sin(x)sinh(y) gives v = cos(x)sinh(y) + g(y)
• Putting these together, v = cos(x)sinh(y) + c
• Our function is u+ vi = sin(x)*cosh(y) + cos(x)sinh(y)i + ci, where c is a real constant.