I have the next exponentiation of complex number $$z ={(1+ i\sqrt 3)}^{2020}$$ I was using the Theorem of Moivre but I got a $$2 ^ {2020}$$ Then how can I get this exponentation without computer calculations? or how can I that power?
2026-04-28 13:43:59.1777383839
Complex large exponentiation
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Hint: $1+\sqrt{3}i= 2\left(\cos \frac{\pi}{3} + i\sin \frac{\pi}{3}\right)$. Note that the right answer is $2^{2020}\times \text{something}$, and this "something" is the outcome of the De Moivre's formula that you are trying to use.