(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
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
I showed the question in the upload photo.
I want you to prove (d,e,f) parts
Thank you very much !
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.
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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