Proving Trigonometric Ratios by Complex Numbers Q2
Proving Trigonometric Ratios by Complex Numbers Q2
Evaluate the product \(\frac{1+\mathbf{i}}{1+\sqrt{3}\mathbf{i}}\). Deduce that \(\tan \left( \frac{\pi }{12} \right)=2-\sqrt{3}\).
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Answer:Cartesian: \((1 - \sqrt{3}) + (1 + \sqrt{3})i\), Exponential: \(2\sqrt{2} e^{i\frac{7\pi}{12}}\), \(\tan \frac{7\pi}{12} = -(2 + \sqrt{3})\)
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