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Evaluate

$$\left ( \frac{1+\sqrt{3}}{2\sqrt{2}}+ i \frac{\sqrt{3}-1}{2\sqrt{2}} \right )^{72}$$

Maybe this form \[\left ( \frac{1+\sqrt{3}}{2\sqrt{2}}+ i \frac{\sqrt{3}-1}{2\sqrt{2}} \right )^{72}=\Big(\cos\tfrac{\pi}{12}+i\sin\tfrac{\pi}{12}\Big)^{72}\] is helpful...