Without the use of a calculator, express $\frac{1}{3}-\frac{\sqrt{3}}{3}\mathrm{i}$ and $1-\mathrm{i

Question

Without the use of a calculator, express $\frac{1}{3}-\frac{\sqrt{3}}{3}\mathrm{i}$ and $1-\mathrm{i}$ in exponential form. Hence evaluate ${{\left( \frac{\frac{1}{3}-\frac{\sqrt{3}}{3}\mathrm{i}}{1-\mathrm{i}} \right)}^{12}}$.

Accepted Answer

$ -\frac{2^6}{3^{12}} $ or $ -\frac{64}{531441} $

Properties from Exponential or Trigonometric form Q4

Properties from Exponential or Trigonometric form Q4

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