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Question Number 48226 by gunawan last updated on 21/Nov/18

$$\mathrm{calculate}$$$$\log {(-1+\sqrt{3}\mathrm{i})}^2$$

Answered by Smail last updated on 21/Nov/18

$$ln\left({(-1+\sqrt{3}i)}^2\right)=2ln\left(2(-\frac{1}{2}+i\frac{\sqrt{3}}{2})\right)$$$$=2ln2+2ln(cos\left(\frac{2\pi }{3}\right)+isin\left(\frac{2\pi }{3}\right))$$$$=2ln2+2ln\left(e^{i\frac{2\pi }{3}}\right)=2ln2+i\frac{4\pi }{3}$$

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