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19.9. Use Equations (19.5) and (19.6), to establish the following identities: (a) Re(sin z) = sin x cosh (b) Re(cos z) (c) Re(sinh z) = sinh x cos y, Im(sin z) = cOs x sinh y. Im(cos z) = – sin x sinh y. Im(sinh z) = cosh x sin y. Y, = COs x cosh y, %3D

19.9. Use Equations (19.5) and (19.6), to establish the following identities: (a) Re(sin z) = sin x cosh (b) Re(cos z) (c) Re(sinh z) = sinh x cos y, Im(sin z) = cOs x sinh y. Im(cos z) = – sin x sinh y. Im(sinh z) = cosh x sin y. Y, = COs x cosh y, %3D

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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hi

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

Thank you very much.

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.
Transcribed Image 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.
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
Transcribed Image 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
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