Use the Euler relation to split a function into complex and imaginary parts
11 views (last 30 days)
Show older comments
Sergio Manzetti
on 2 Jan 2018
Commented: Sergio Manzetti
on 2 Jan 2018
Hi, I found a thread considering to split a function into Re and Im, and used it's command:
if true
% code
end
y = C*exp(-(x*(g*i + (- 2*g^2 + E)^(1/2)))/h) + exp((g*i - (- 2*g^2 + E)^(1/2))/h)*exp(-(x*(g*1i - (- 2*g^2 + E)^(1/2)))/h)*(pi - C*exp(-(g*1i + (- 2*g^2 + E)^(1/2))/h))
y = rewrite(y, 'sincos')
Ref = simplify(collect(real(y))) % Real part
Imf = simplify(collect(imag(y))) % Imaginary part
however, the result does not split Im and Re parts:
Ref =
real((cos((524288*x*(67108864*15769878386734594^(1/2) - 5959077882784213))/616503364953199) + sin((524288*x*(67108864*15769878386734594^(1/2) - 5959077882784213))/616503364953199)* 1i)*(cos((35184372088832*15769878386734594^(1/2))/616503364953199 - 3124273025009169465344/616503364953199) - sin((35184372088832*15769878386734594^(1/2))/616503364953199 - 3124273025009169465344/616503364953199)* 1i)*(pi - C*cos((35184372088832*15769878386734594^(1/2))/616503364953199 + 3124273025009169465344/616503364953199) + C*sin((35184372088832*15769878386734594^(1/2))/616503364953199 + 3124273025009169465344/616503364953199)*1i)) + real(C*(cos((524288*x*(67108864*15769878386734594^(1/2) + 5959077882784213))/616503364953199) - sin((524288*x*(67108864*15769878386734594^(1/2) + 5959077882784213))/616503364953199)*1i))
Imf =
imag((cos((524288*x*(67108864*15769878386734594^(1/2) - 5959077882784213))/616503364953199) + sin((524288*x*(67108864*15769878386734594^(1/2) - 5959077882784213))/616503364953199)*1i)*(cos((35184372088832*15769878386734594^(1/2))/616503364953199 - 3124273025009169465344/616503364953199) - sin((35184372088832*15769878386734594^(1/2))/616503364953199 - 3124273025009169465344/616503364953199)*1i)*(pi - C*cos((35184372088832*15769878386734594^(1/2))/616503364953199 + 3124273025009169465344/616503364953199) + C*sin((35184372088832*15769878386734594^(1/2))/616503364953199 + 3124273025009169465344/616503364953199)*1i)) + imag(C*(cos((524288*x*(67108864*15769878386734594^(1/2) + 5959077882784213))/616503364953199) - sin((524288*x*(67108864*15769878386734594^(1/2) + 5959077882784213))/616503364953199)*1i))
Is this a technicallyimpossible case?
Thanks
0 Comments
Accepted Answer
John D'Errico
on 2 Jan 2018
Edited: John D'Errico
on 2 Jan 2018
You CANNOT use real and imag as you have done. At least, it will be a waste of time.
A quick glance shows that at least C and x are still symbolic variables. What values do they take on? Who knows? So segregating a long expression that includes those variables into real and imaginary parts is impossible.
Depending on the values of C and x (and maybe some other variables that I missed) all it can say is that the real part is real(*stuff*) and the imaginary part is imag(*stuff*). That is exactly what the symbolic toolbox returned.
Addendum: you can use vpa to simplify the expression, resolving some of the nasty looking numbers. But until explicit numeric values for C and x are supplied, you cannot reduce the result into real and imaginary parts.
More Answers (1)
Walter Roberson
on 2 Jan 2018
If you add assumptions to the symbolic variables then MATLAB can potentially do the appropriate separation. In particular you can use
syms x real
to add an assumption of real value to x
See Also
Categories
Find more on Assumptions in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!