Discussion
For complex roots \( \alpha \pm i\beta \), the complementary function is
Answer: C
The pair \( e^{(\alpha \pm i\beta)x} \) combines through Euler's formula into a real exponential envelope times an oscillation:
\[ y \;=\; e^{\alpha x}\left(C_{1}\cos\beta x + C_{2}\sin\beta x\right). \]
The real part sets the growth or decay and the imaginary part the frequency, so interchanging them would exchange the envelope for the oscillation
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