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**MathIsOhSoHard** I know that in a complex number such as

$\displaystyle z=a+bi$

"Re" is supposed to be the "real part", which is $\displaystyle a$ so that $\displaystyle Re(a+bi)=a$ and that "Im" is supposed to be the "imaginary part", which is $\displaystyle b$ so that $\displaystyle Im(a+bi)=b$ in the above example.

However, recently I stumpled upon a problem when trying to solve linear systems:

$\displaystyle y(t)=Re(H(i\omega)e^{i\omega t})$

I'm not sure that I understand how exactly to execute this formula with the "Re" part.

Here is an example:

$\displaystyle Re\left( \frac{-3+4i}{25}\cos(t)+i\cdot\sin(t) \right)=\frac{-3}{25}\cos(t)-\frac{4}{25}\sin(t)$