How to solve a complex equation which has one equation but two real variables?

Normally, a set of equations that have the same number of unknowns can be solved. However, an complex eqaution with two unknowns are possible to be solved. For example, a complex equation like : x+y*j = a+ b*j, can be solved by x = a, and y = b, because the real part and imaginary part correspond to each other.

Now, my question is how to do it with MATLAB solve function. A typical scanerio is the propagation constant solution in EM wave. The original eqaution is:

Kc = omiga* sqrt(u*(eps-j*sigma/omiga));

we would like to solve the equation into Kc = k_real -j* k_img. k_real and k_img are the unknowns in the equation.

Answer 1

[Torsten]

Does that help ?

>> syms z k
>> z0 = 1+3*1I;
>> a = solve(z==k*z0,z)
a = (sym) k*(1 + 3*I)
>> real(a)
ans = (sym) re(k) - 3*im(kc)
>> imag(a)
ans = (sym) 3*re(k) + im(kc)

[madhan ravi]

Feng Zhou's answer moved here:

I get the results like this. There are also something strange in my Matlab. I suppose there are something wrong in my MATLAB。

>> syms z k 
>> z0 = 1+3*1i;
>> a = solve(z==k*z0,z)
a =
 
                                       z

[madhan ravi]

>> syms z  complex 
         % ^^^^^^^---- add the assumption  
>> syms k 
>> z0 = 1+3*1i;
>> a = solve(z==k*z0,z)

a =
 
k*(1 + 3i)
 
>> real(a)
 
ans =
 
real(k) - 3*imag(k)
 
>> imag(a)
 
ans =
 
imag(k) + 3*real(k)
 
>> 

[Walter Roberson]

complex is the default assumption and does not need to be added. Instead add real to the variables intended to be real valued.

Answer 2

[Walter Roberson]

split the equation into two parts by taking real() and imag() so you end up with two equations in two unknowns .