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(d) Re(cosh z) = cosh x cos y, Im(cosh z) = sinh a sin y. (e) | sin z|? = sin² x + sinh? y, (f) | sinh z|2 = sinh? x + sin? y, | cos z|2 = cos² x + sinh? y. %3D %3D |cosh z|2 = sinh x + cos² y.

(d) Re(cosh z) = cosh x cos y, Im(cosh z) = sinh a sin y. (e) | sin z|? = sin² x + sinh? y, (f) | sinh z|2 = sinh? x + sin? y, | cos z|2 = cos² x + sinh? y. %3D %3D |cosh z|2 = sinh x + cos² y.

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 numbers.

I showed the question in the upload photo.

I want you to prove (d,e,f) parts

Thank you very much !

19.9. Use Equations (19.5) and (19.6), to establish the following identities: Im/ COSII Y, COD A Rolsinh )– sinh xc ) – cosh (d) Re(cosh z) = cosh x cos y, Im(cosh z) = sinh x sin y. (e) | sin z|2 = (f) | sinh z|2 = sinh? x + sin? y, sin? x + sinh? y, | cos z|2 = cos² x + sinh? y. COS | cosh z|2 = sinh“ x + cos y.
Transcribed Image Text:19.9. Use Equations (19.5) and (19.6), to establish the following identities: Im/ COSII Y, COD A Rolsinh )– sinh xc ) – cosh (d) Re(cosh z) = cosh x cos y, Im(cosh z) = sinh x sin y. (e) | sin z|2 = (f) | sinh z|2 = sinh? x + sin? y, sin? x + sinh? y, | cos z|2 = cos² x + sinh? y. COS | cosh z|2 = sinh“ x + cos 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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