Cannot solve a hyperbolic equation

Hi,

I am trying to solve following equation using Matlab:

And here is my code:

syms z g;
eq1=z*sinh(790*g)==(12.3+i*1.49*10^-3);
eq2=tanh(395g)==z*(1.8*10^-9);
solve(eq1,eq2,z,g)

but I get following error:

Warning: Cannot solve symbolically. Returning a numeric approximation instead. 
> In solve at 306 

ans = 

      z: [1x1 sym]
      g: [1x1 sym]

What I am doing wrong here?

Answer 1

[Star Strider]

For one, you left out a multiplication operator (*) in ‘eq2’. The numeric output is appropriate, since you’re identifying ‘Z0’ and ‘gamma’.

The code (corrected):

syms z g;
eq1=z*sinh(790*g)==(12.3+1i*1.49E-3);
eq2=tanh(395*g)==z*(1.8E-9);
[z,g] = solve(eq1,eq2,z,g)

produces:

z =

58452.259506186817111402883076281 + 3.5404010317307016714429740047407i

g =

0.00000026636472784652195740050195875373 + 0.000000000016133473234585554676003727620685i

Use the vpa or vpasolve functions if you don’t want quite so many digits.

Answer 2

[John D'Errico]

Why must it be that you did something wrong? Must a symbolic solution exist for all problems? No.

So it gave you a numerical solution. Did you look at what it returned? Does the solution satisfy the equations you have posed?

That was NOT an error anyway, but a warning.