Use "Solve" function to find certain value of magnitude of complex function

I have a function with complex variable. I want to get the value of "s" at which the magnitude of the function equals certain value (e.g. 10).

I use "abs" to get the magnitude of the function, then use "solve". If I get the magnitude by using sqrt(real^2+imag^2) I et different answer (actually the one that I need).

However, when I plot both magnitudes, the results are the same.

Code is here:

syms s;

y = 10/((j*s)^2+(j*s)+1);

mag_sqrt = sqrt((real(y))^2+(imag(y))^2);

mag_abs = abs(y);

solve_abs  = double(solve(20*log10(mag_abs)==10))  %    answer = 0.0000 + 2.0532i , 0.0000 - 1.0532i (wrong answer)

solve_sqrt = double(solve(20*log10(mag_sqrt)==10)) %    answer = 1.8819, -1.8819 (Correct answer)

ezplot(20*log10(mag_sqrt),0.1,100); grid on;

ezplot(20*log10(mag_abs),0.1,100); grid on;

phase = (180/pi)*double(subs(angle(y),s,solve_abs))  % answer = 0 (Wrong answer)

phase = (180/pi)*double(subs(angle(y),s,solve_sqrt)) % answer = -143.4806 , 143.4806 (Correct answer)

Answer 1

[Walter Roberson]

syms s real

When you ask solve to solve a non-polynomial with multiple roots then it will return either a parameterized solution or else it will solve numerically. You did not constrain the range of values so it happened to decide to pick an imaginary valued solution. Forcing real values has a better chance of getting one of the two values you are expecting.

[inframeedo]

I tried both definitions:

syms s real

and

syms s positive

I get this error:

Error using eval
Undefined function or variable 'NIL'.

Error in sym/double (line 828)
        X = eval(Xstr);

[Walter Roberson]

syms s real
y = 10/((j*s)^2+(j*s)+1);
mag_sqrt = simplify(sqrt((real(y))^2+(imag(y))^2), 'steps', 20)
double(solve(20*log10(mag_sqrt)==10))