Can I separate a symbolic expression into real and imaginary components?

I am trying to solve a system of equations for a Vibrations problem. The matrices have one symbolic variable (w), real and imaginary components. I solve the system equation using basic matrix math, and it gives my output is in the following form:

(w*(- 340681500621583831516475 + 245114682516134139416800*i) - 2^(1/2)*w*161744841465528059953152*i + 10845775541925882888192*2^(1/2)*w^2 + 2^(1/2)*w^3*3616953450731929600*i + w^2*(- 76906298945748700000 - 11075142634881799717775*i) + 3948349625585861875*w^3 + 3922540001147731586120800 + 2633460286177396815135200*i)/(2560*(w^4*(1099511627776000*i) + 3407162234105757696*w^3 + w^2*(-71889311507307749723*i) - 584836757809722693890*w + 4461121651825735176160*i))

which is a total mess. Is there a way that I can get MATLAB to put that output in the following form?:

= [(equation in terms of w) + (equation in terms of w)*i]

Any help would be appreciated. Thanks!

Answer 1

[Ishu]

Hi Anthony,

In order to separate real and imaginary parts from an equation you can make use of "real" and imag" functions of MATLAB. You can refer to the below example.

syms w
y = 3 + 4i + w*5.5i;
y_imag = imag(y)

y_imag = 

y_real = real(y)

y_real = 

You can also use "simplify" function to further simplify your equations and to have a more clear visualization.

Below are the documentaion links you can refer to:

real - https://www.mathworks.com/help/matlab/ref/real.html?searchHighlight=real&s_tid=srchtitle_support_results_1_real

imaginary - https://www.mathworks.com/help/matlab/ref/imag.html?searchHighlight=imaginary&s_tid=srchtitle_support_results_7_imaginary

Hope it helps!