dz 19.9. Use Equations (19.5) and (19.6), to establish the following identities: Im(sin z) (a) Re(sin z) = sin x cosh y, (b) Re(cos z) : = COs x sinh y. COS Z = COS x Cosh y, Im(cos z) - sin x sinh Y....

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My question is about Complex Derivative and Integral. I showed the picture in the upload photos.The first photo is the guide and the second is the question itself

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Extracted text: dz 19.9. Use Equations (19.5) and (19.6), to establish the following identities: Im(sin z) (a) Re(sin z) = sin x cosh y, (b) Re(cos z) : = COs x sinh y. COS Z = COS x Cosh y, Im(cos z) - sin x sinh Y. (c) Re(sinh z) = sinh x cos y, Im(sinh z) = cosh x sin y. (d) Re(cosh z) = cosh x cos y, Im(cosh z) = sinh x sin y. (e) | sin z|2 = sin? x + sinh? y, (f) | sinh z|² = sinh x + sin? y, | cos z|2 = cos“ x + sinh² y. cos? | cosh z|2 = sinh² x + cos² y.


Extracted text: eiz – e-i: eiz +e-iz sin z and COS Z (19.5) 2i 2 e - e e? +e-2 sinh z and cosh z = (19.6) 2 2