calculate-log-1-3-i-2-

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

calculate

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

Answered by Smail last updated on 21/Nov/18

l n ({(- 1 + \sqrt{3} i)}^{2}) = 2 l n (2 (- \frac{1}{2} + i \frac{\sqrt{3}}{2}))

= 2 l n 2 + 2 l n (c o s (\frac{2 π}{3}) + i s i n (\frac{2 π}{3}))

= 2 l n 2 + 2 l n (e^{i \frac{2 π}{3}}) = 2 l n 2 + i \frac{4 π}{3}

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