Finding the points where a complex function is real-valued

Question

I have defined the following complex system:

syms x 
sys(x) = ((10+1.*i.*x))/(20+(5.*i.*x)+((10.*i.*x).^2))+((1.*i.*x).^3); 
ImaginaryPart = imag(sys)

MATLAB returned the following results:

ImaginaryPart(x) =

- real(x^3) + imag((10 + x*1i)/(- 100*x^2 + x*5i + 20))


RealPart(x) =

- real(x^3) + imag((10 + x*1i)/(- 100*x^2 + x*5i + 20))

Now for which value of x will ImaginaryPart(x) be 0? (i.e. ImaginaryPart(x)= 0)?

Answer 1

As @AndrasDeak commented, solve will do the trick for you:

S = solve(ImaginaryPart(x)== 0,x);