Hello, I'm dealing with the following equation:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]A e^{jat} + B e^{jbt} = C e^{jct}[/tex] [tex] \forall t \in \mathbb{R}[/tex]

My book says: given nonzero constants A,B,C, if the above equation yelds for any real t, then the a,b,c constants must be equal.

The above statement is prooved by taking the Fourier transform of the complex exponentials:

[tex]A2\pi \delta(t+a) + B2\pi \delta(t+b) = C2\pi \delta(t+c)[/tex][tex]A \delta(t+a) + B \delta(t+b) = C \delta(t+c)[/tex]

But I don't really get how such an equation as the last one can force a,b,c to be equal.

Any help would be appreciated, thanks in advance.

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# Solving an equation with Dirac delta functions

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