Using Complex Numbers to Deduce Trigonometric Values
Using Complex Numbers to Deduce Trigonometric Values
TGM Original Questions
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:\(\text{Quotient:}\hspace{0.5em}\dfrac{1+\sqrt{3}}{4}+\dfrac{1-\sqrt{3}}{4}\mathbf{i}\) \(\text{Hence:}\hspace{0.5em}\tan\left(\dfrac{\pi}{12}\right)=2-\sqrt{3}\)
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