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Say one wants to find the inverse Laplace Transform of a function, and the method for attaining the solution is executed via partial fractions. Do the real numbers go with the complex numbers when determining the constants of partials? Perhaps this is wordy. I'll provide a theoretical example:

Say we have:

[tex]\frac{A}{s+1-\sqrt{3}j}+\frac{B}{s+1+\sqrt{3}j}[/tex] where A+B=s+2.

Do we say:

[tex]A(1+\sqrt{3}i)+B(1-\sqrt{3}i)=2[/tex]

or are the complex numbers treated separately?