Question

1. Test the analyticity of the function w = In(z) and find its derivative​

Answer 1

Answer:

This follows by writing sin z as

sinx. cosh y + i cosx. sinh y = u(x,y) + i v(x,y) and then noting that u, v satisfy the Cauchy-Riemann conditions u_x = v_y and u_y = - v_x for all (x,y) and that all four first partial derivatives are continuous everywhere.

Answer 2

Answer:

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