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duplicate.
It was solved yesterday under this link
https://www.algebra.com/algebra/homework/complex/Complex_Numbers.faq.question.1172367.html
https://www.algebra.com/algebra/homework/complex/Complex_Numbers.faq.question.1172367.html
Could you explain me please for WHAT REASON do you post this duplicate problem again ?
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By the way, the problem formulation is not correct in your post.
The correct formulation is THIS:
if f = u + iv is an analytic function and u = Sin(x)*Cosh(y), then find v.
It is VERY serious fault, which shows that the person who created this "problem" DOES NOT KNOW the subject.