How to solve COSH(complex number)?

cosh(a+jb)

Say x = 0.00931 + j0.3730
Can we solve:
cosh(x)
... directly using sciencetific calculator, e.g. CASIO fx-570MS?

Thanks.

cosh complex number

I've just tried it on my FX570MS calculater and it didn't work, better do it on hand
That'll be:
cosh(a+jb)=(exp(a)*exp(jb)+exp(-a)*exp(-jb))/2
=0.5exp(a)[cos(b)+jsin(b)]+0.5exp(-a)[cos(b)-jsin(b)]
=0.5cos(b)(2*cosh(a))+0.5j(2*sin(b)*sinh(a))
=cos(b)cosh(a)+jsin(b)cosh(a);

But the calculator can't do that!

solving cosh

elmolla, agree with you... fx-570MS showed Math ERROR when performing the calculation...

Tested with Matlab just now... We could solve cosh(a+jb) directly

ti voyage cosh

elmolla said:

I've just tried it on my FX570MS calculater and it didn't work, better do it on hand
That'll be:
cosh(a+jb)=(exp(a)*exp(jb)+exp(-a)*exp(-jb))/2
=0.5exp(a)[cos(b)+jsin(b)]+0.5exp(-a)[cos(b)-jsin(b)]
=0.5cos(b)(2*cosh(a))+0.5j(2*sin(b)*sinh(a))
=cos(b)cosh(a)+jsin(b)cosh(a);

But the calculator can't do that!

Click to expand...

very few calculator can do it without own programming or installing extra package, special if you want small size pocket calculators (only hp42S??)

I know:

hp28s
hp42s
hp48 (all variant)
hp49 (all variant)
possibly T89

anybody know more calculators with complex support including complex hyperbolic
support and also handle asin(2) without error/exeption ?

make matrice with complex number is also very nice..

make a list!

solve cosh

I'll report the results from my quarter-century old HP-15C when I find it. I recall that calcultor (in complex mode) able to perform such clculations.

complex cosh

LouisSheffield said:

I'll report the results from my quarter-century old HP-15C when I find it. I recall that calcultor (in complex mode) able to perform such clculations.

Click to expand...

I know hp33s not support complex hyperbolic, but possible make via writing program and using complex mode of y^x, e^x and ln + lot of storing register (stack is not deep enough)...


hp 15c -> hp32sii -> hp33s, hp15c possible not handle complex hyperbolic by default


hp28s-----\
hp41cv----+----> hp42s -> hp48s -> hp48sx -> hp48g -> 48gx -> hp49g -> hp49g+

all this hp models (hp41cv with extra lib) handle complex number very well, including hyperbolic.


TI89 possible?
TI92 possible?
TI voyage possible ?
Casio classpad possible ??

more ?

how to solve cosh

The HP-15C (complex mode) has the cosh answer as
0.931278664 + j 0.003392713
( wooo hoooo!!! )

ti 92 cosh(x)

LouisSheffield said:

The HP-15C (complex mode) has the cosh answer as
0.931278664 + j 0.003392713
( wooo hoooo!!! )

Click to expand...

Impressive!! Why cannot hp32sii and hp33s handle this by default ???!!!

How hp15 C handle asin(2) - give complex answer ???

(asin(2) = 1.5708+j1.3170)

---

And, when in time make hp new usable replacement for hp15c and hp42s in same small size with full complex support on all math functions as old machine to solve this above 'simple' calculating ???

Only big size, low quality (compare to old hp:s) and battery eating hp48g+ and hp49+ in market nowadays, can handle above very 'simple ' problem, not of hp:s small calculators...

I think in time before I look after replacement of hp42s for my job, every scientific calculator worth the name should solve above and other complex number problem easy as standard now year 2006, same as advanced calculator done easly before 1988 (hp 15c, hp41CV, hp42S) - but no... I'ts more or less same status as ugly TI57 and TI30 in beginning of 80's exept LED on display replaces with LCD...

cosh complex

The 15C actually gives the complex conjugate of your answer (i.e. 1.5708-j1.3170), but it DOES it!

There's actually a site devoted to petitioning HP for their reintroduction: https://www.hp15c.org/
(that's where I downloaded its manual so I could figure out how to enter the imaginary part.

Also (not plugging them), Lygea has a 15C emulator for PocketPC. I would HOPE that its behavior is the same as the real thing relative to these problems.

cosh of complex number by hand

LouisSheffield said:

The 15C actually gives the complex conjugate of your answer (i.e. 1.5708-j1.3170), but it DOES it!

There's actually a site devoted to petitioning HP for their reintroduction: h**p://www.hp15c.org/
(that's where I downloaded its manual so I could figure out how to enter the imaginary part.

Also (not plugging them), Lygea has a 15C emulator for PocketPC. I would HOPE that its behavior is the same as the real thing relative to these problems.

Click to expand...

I'm. impressive hp 15 C also can do it!, it's very rare in calculator world and only knows on HP28S, hp42S, hp48x, hp49x, now on hp15C and possible TI89.

hp-emulator people is more or less fanatic to emulate hp-calculators 'perfect' - so, if works in emulator (ie emulate prom), is also working in real thing.

My solution to replace physical hp42s just now in my job, is using free42 (simulator!, not emulator of copyrigthed prom) on PC and palm-T (no yet for pocket PC), it works, but not same as real thing (miss real button on pda)