Proving complex with hyperbolic

[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 statement induces that hyperbolics should be involved.

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

 

[HallsofIvy]

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!)

 

[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)

 

[HallsofIvy]

Union regulation?

 

[barnaby2]

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