*24*

*Complex variables*

**24.1***Find an analytic function of* *z* = *x* + *iy* *whose imaginary part is*

If the required function is *f*(*z*) = *u* + *iv*, with *v* = (*y* cos *y* + *x* sin *y*) exp *x*, then, from the Cauchy–Riemann equations,

Integrating with respect to *y* gives ...

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