using cosh and inverse cosh in matlab

Hi all

i have problem using cosh and cosh^-1 in matlab . in my program i have to solve complex number using cosh and i have to reused cosh^-1 to get the same number but i couldnt . for example

A=5+5i

B= cosh(A) it gives (21.0506 -71.1553i)

A=acosh(B) it gives (5.0000 - 1.2832i) which is not the same A (5+5i)

how can i solve this problem

thank you

Answer 1

[Steven Lord]

What problem?

A1 = 5+5i

A1 = 5.0000 + 5.0000i

A2 = acosh(cosh(A1))

A2 = 5.0000 - 1.2832i

(A2-A1)/(2i*pi)

ans = -1

Remember that as stated on Wikipedia "hyperbolic functions are periodic with respect to the imaginary component, with period " So you received a correct answer (if you added one period, , to A2 you get A1 or close enough) even if it wasn't the correct answer you expected.

A1 - (A2 + 2i*pi)

ans = 0

[mohammed hussein]

Thank you very much for your answer. The problem is to find the original number after using a hyperbolic function (cosh). Theoretically, when I have the results of (cosh) and I want the original number before (cosh), I used the inverse of cosh (acosh).

As I explain in the example , If I have this complex number A=5+5i and I only have the result of cosh(A) which is (21.0506 -71.1553i). but I want the A (original number) so I normally use the inverse of cosh, A=acosh(B) which is in MATLAB (5.0000 - 1.2832i). the result of MATLAB is a different number than what I used in beginning (A=5+5i).

My question is how can I use the acosh of complex numbers from the result of cosh to find the original number (A) without error especially in the imaginary part . The most important is to find A because i only have results of cosh

Thank you again for your answer

[Steven Lord]

Without more information, you can't.

As a simpler example, I'm thinking of a number that gives the result 4 when squared. What is my number?

You may say that the answer is 2. That is one correct answer. A different correct answer is -2.

It is impossible for you to tell whether the number I was thinking of was 2 or -2.