Proving complex with hyperbolic

1. Dec 9, 2007

barnaby2

i have a problem in my engineering maths which says as follows:

show that if z is a complex number then

2 cos (x) = z + 1 / z

and 2 j sin (x) = z - 1/z

given that cosh (jy) = cos (y) and sinh (jy) = j sin(y)

I can solve the problem without using the hyperbolics but that last statment induces that hyperbolics should be involved.

does anyone know how to use the hyperbolics to solve this problem?

2. Dec 9, 2007

HallsofIvy

Staff Emeritus
First, when asking for help on a problem like this, it would be a really good idea to specify that z= x+ iy!

Use the fact that cosh(t)= $(e^t+ e^{-t})/2$ and sinh(t)= $e^t- e^{-t}$. Those, together with $e^{jy}= cos(y)+ j sin(y)$ should do it.

(I can't tell you how much it hurt to write "j" instead of "i". I just cringe at jmaginary numbers!)

3. Dec 9, 2007

barnaby2

thanks hallsofivy. i now understood the question.

(i am sorry to inflict you pain with j but we engineers are not allowed to call it i)

4. Dec 10, 2007

HallsofIvy

Staff Emeritus
Union regulation?

5. Dec 10, 2007

barnaby2

No.. just for not creating any fights between currents and complex.....which can turn in a very dangerous situation