Find the value of $(1 + i\sqrt{3})^5 + (1 - i\sqrt{3})^5$.
Step-by-Step Solution
Key Concept: Write $1+i\sqrt{3} = 2e^{i\pi/3}$, so $(1+i\sqrt{3})^5 = 32e^{5i\pi/3}$. Add to its conjugate and use $2 \cos(5\pi/3)$.
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Correct Answer: 32