Question 1020785
*[tex \large 1 + i \sqrt{3}] can be rewritten as *[tex \large 2e^{i \frac{\pi}{3}}] using Euler's formula (since the magnitude and argument are 2 and pi/3 respectively).


Then *[tex \large (1 + i \sqrt{3})^6 = (2e^{i \frac{\pi}{3}})^6 = 64e^{i \cdot 2 \pi} = 64].