# How to Tanh(complex number)

1. ### trustnoone

17
As the title shows, I want to do they hyperbolic tan of a complex number, using my calculator (casio fx100ms) but I keep getting a maths error, whether I do it using the tanh function or if I try the

(1-e^(-2x))/(1+e^(-2x))

Any help would be awesome. Thanks.

### Staff: Mentor

1 person likes this.
3. ### trustnoone

17
Nooooo :(, thanks for looking into it mate, I thought it was just something I was doing wrong. Is there any way I can do it normally? like any way I can do it say like the hard way?

### Staff: Mentor

Use google, in the search box enter tanh(5i) as an example and google calculator will show the answer - 3.38051501 i

5. ### SteamKing

8,870
Staff Emeritus
Dang calculators only support real numbers! (Well, most of 'em anyways)

Tanh(z) can be evaluated by using the definition of the tanh function with complex argument z,

tanh(z) = sinh(z) / cosh(z) = $\frac{e^{z}-e^{-z}}{e^z+e^{-z}}$

which is not as easy to calculate as it looks. See:

http://www.uni-graz.at/imawww/vqm/pages/complex/12_tanh.html

You can always use Wolfram Alpha to calculate a tanh(z) for a specific value of z

1 person likes this.
6. ### trustnoone

17
Thanks mate, its actually on my formula sheet on my exam I got to take tomorrow, but if thats the case I really don't think I will be able to use it with only my calculator itself. Cheers though.

### Staff: Mentor

Perhaps you should ask your teacher about it before the exam. You might need a better calculator TI-83 ??? but not sure if it has the same limit or not.

CORRECTION:

http://tibasicdev.wikidot.com/tanh

TI caclculator doesn't support complex numbers with tanh either.