How to Tanh(complex number)

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In summary, the conversation discusses the difficulty of calculating the hyperbolic tangent of a complex number using a Casio calculator. The calculator's manual states that it does not support complex numbers for this function. Some suggestions are made, such as using Google or Wolfram Alpha to calculate the value, or using a different calculator that may support complex numbers. However, the individual may need to consult their teacher before using these methods on an exam.
  • #1
trustnoone
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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.
 
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  • #3
jedishrfu said:
I think your calculator manual says that the calculator doesn't support the complex number coefficient mode for hyperbolic sinh, cosh, tanh and other select functions.

http://www.google.com/url?sa=t&rct=...ttcjO3x9gBVXwPw&bvm=bv.69411363,d.cWc&cad=rja

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?
 
  • #4
Use google, in the search box enter tanh(5i) as an example and google calculator will show the answer - 3.38051501 i
 
  • #5
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) = [itex]\frac{e^{z}-e^{-z}}{e^z+e^{-z}}[/itex]

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

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

You can always use Wolfram Alpha to calculate a tanh(z) for a specific value of z
 
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  • #6
SteamKing said:
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) = [itex]\frac{e^{z}-e^{-z}}{e^z+e^{-z}}[/itex]

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

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

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

Thanks mate, its actually on my formula sheet on my exam I got to take tomorrow, but if that's the case I really don't think I will be able to use it with only my calculator itself. Cheers though.
 
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  • #7
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.
 

1. What is the definition of tanh(z)?

Tanh(z) is a mathematical function that maps a complex number, z, to another complex number. It is defined as (e^z - e^-z)/(e^z + e^-z), where e is the base of the natural logarithm.

2. How do I calculate the value of tanh(z)?

To calculate the value of tanh(z), you can use a scientific calculator or a computer program with a built-in tanh function. You can also use the definition of tanh(z) and plug in the value of z to calculate it manually.

3. What is the range of tanh(z)?

The range of tanh(z) is from -1 to 1, where -1 is the value when z approaches negative infinity and 1 is the value when z approaches positive infinity.

4. What are the properties of tanh(z)?

Some properties of tanh(z) include: it is an odd function, meaning tanh(-z) = -tanh(z); it is an entire function, meaning it is analytic at every point in the complex plane; and it satisfies the identity tanh(z) = sinh(z)/cosh(z).

5. How is tanh(z) used in science and engineering?

Tanh(z) is used in various fields of science and engineering, such as signal processing, control systems, and quantum mechanics. It is also used in statistics to transform data to have a more normal distribution, and in neural networks as an activation function. Additionally, it has applications in physics, specifically in the study of black holes and solitons.

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