Question
Suppose $A e^{i a x}+B e^{i b x}=C e^{i c x},$ for some nonzero constants $A, B, C, a, b$.$c,$ and for all $x .$ Prove that $a=b=c$ and $A+B=C$.
Step 1
Step 1: Given the equation $A e^{i a x}+B e^{i b x}=C e^{i c x}$, we can rewrite $e^{i \theta}$ as $\cos \theta + i \sin \theta$ using Euler's formula. Show more…
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